Solve (x-4)(x-8)-2x(4x-5)

Question

Simplify the expression

- 7 x^{2} - 2 x + 32

Evaluate

(x - 4) (x - 8) - 2 x (4 x - 5)

Expand the expression

More Steps

Calculate

(x - 4) (x - 8)

Apply the distributive property

x \times x - x \times 8 - 4 x - (- 4 \times 8)

Multiply the terms

x^{2} - x \times 8 - 4 x - (- 4 \times 8)

Use the commutative property to reorder the terms

x^{2} - 8 x - 4 x - (- 4 \times 8)

Multiply the numbers

x^{2} - 8 x - 4 x - (- 32)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x^{2} - 8 x - 4 x + 32

Subtract the terms

More Steps

Evaluate

- 8 x - 4 x

Collect like terms by calculating the sum or difference of their coefficients

(- 8 - 4) x

Subtract the numbers

- 12 x

x^{2} - 12 x + 32

x^{2} - 12 x + 32 - 2 x (4 x - 5)

Expand the expression

More Steps

Calculate

- 2 x (4 x - 5)

Apply the distributive property

- 2 x \times 4 x - (- 2 x \times 5)

Multiply the terms

More Steps

Evaluate

- 2 x \times 4 x

Multiply the numbers

- 8 x \times x

Multiply the terms

- 8 x^{2}

- 8 x^{2} - (- 2 x \times 5)

Multiply the numbers

- 8 x^{2} - (- 10 x)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 8 x^{2} + 10 x

x^{2} - 12 x + 32 - 8 x^{2} + 10 x

Subtract the terms

More Steps

Evaluate

x^{2} - 8 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 8) x^{2}

Subtract the numbers

- 7 x^{2}

- 7 x^{2} - 12 x + 32 + 10 x

Solution

More Steps

Evaluate

- 12 x + 10 x

Collect like terms by calculating the sum or difference of their coefficients

(- 12 + 10) x

Add the numbers

- 2 x

- 7 x^{2} - 2 x + 32

Show Solution

Factor the expression

(- x + 2) (7 x + 16)

Evaluate

(x - 4) (x - 8) - 2 x (4 x - 5)

Simplify

More Steps

Evaluate

(x - 4) (x - 8)

Apply the distributive property

x \times x + x (- 8) - 4 x - 4 (- 8)

Multiply the terms

x^{2} + x (- 8) - 4 x - 4 (- 8)

Use the commutative property to reorder the terms

x^{2} - 8 x - 4 x - 4 (- 8)

Multiply the terms

More Steps

Evaluate

- 4 (- 8)

Multiplying or dividing an even number of negative terms equals a positive

4 \times 8

Multiply the numbers

32

x^{2} - 8 x - 4 x + 32

x^{2} - 8 x - 4 x + 32 - 2 x (4 x - 5)

Simplify

More Steps

Evaluate

- 2 x (4 x - 5)

Apply the distributive property

- 2 x \times 4 x - 2 x (- 5)

Multiply the terms

More Steps

Evaluate

- 2 x \times 4 x

Multiply the numbers

- 8 x \times x

Multiply the terms

- 8 x^{2}

- 8 x^{2} - 2 x (- 5)

Multiply the terms

More Steps

Evaluate

- 2 (- 5)

Multiplying or dividing an even number of negative terms equals a positive

2 \times 5

Multiply the numbers

10

- 8 x^{2} + 10 x

x^{2} - 8 x - 4 x + 32 - 8 x^{2} + 10 x

Subtract the terms

More Steps

Evaluate

x^{2} - 8 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 8) x^{2}

Subtract the numbers

- 7 x^{2}

- 7 x^{2} - 8 x - 4 x + 32 + 10 x

Calculate the sum or difference

More Steps

Evaluate

- 8 x - 4 x + 10 x

Collect like terms by calculating the sum or difference of their coefficients

(- 8 - 4 + 10) x

Calculate the sum or difference

- 2 x

- 7 x^{2} - 2 x + 32

Rewrite the expression

- 7 x^{2} + (- 16 + 14) x + 32

Calculate

- 7 x^{2} - 16 x + 14 x + 32

Rewrite the expression

- x \times 7 x - x \times 16 + 2 \times 7 x + 2 \times 16

Factor out - x from the expression

- x (7 x + 16) + 2 \times 7 x + 2 \times 16

Factor out 2 from the expression

- x (7 x + 16) + 2 (7 x + 16)

Solution

(- x + 2) (7 x + 16)

Show Solution

Find the roots

x_{1} = - \frac{16}{7}, x_{2} = 2

Alternative Form

x_{1} = - 2. \dot{2} 8571 \dot{4}, x_{2} = 2

Evaluate

(x - 4) (x - 8) - 2 x (4 x - 5)

To find the roots of the expression,set the expression equal to 0

(x - 4) (x - 8) - 2 x (4 x - 5) = 0

Calculate

More Steps

Evaluate

(x - 4) (x - 8) - 2 x (4 x - 5)

Expand the expression

More Steps

Calculate

(x - 4) (x - 8)

Apply the distributive property

x \times x - x \times 8 - 4 x - (- 4 \times 8)

Multiply the terms

x^{2} - x \times 8 - 4 x - (- 4 \times 8)

Use the commutative property to reorder the terms

x^{2} - 8 x - 4 x - (- 4 \times 8)

Multiply the numbers

x^{2} - 8 x - 4 x - (- 32)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x^{2} - 8 x - 4 x + 32

Subtract the terms

x^{2} - 12 x + 32

x^{2} - 12 x + 32 - 2 x (4 x - 5)

Expand the expression

More Steps

Calculate

- 2 x (4 x - 5)

Apply the distributive property

- 2 x \times 4 x - (- 2 x \times 5)

Multiply the terms

- 8 x^{2} - (- 2 x \times 5)

Multiply the numbers

- 8 x^{2} - (- 10 x)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 8 x^{2} + 10 x

x^{2} - 12 x + 32 - 8 x^{2} + 10 x

Subtract the terms

More Steps

Evaluate

x^{2} - 8 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 8) x^{2}

Subtract the numbers

- 7 x^{2}

- 7 x^{2} - 12 x + 32 + 10 x

Add the terms

More Steps

Evaluate

- 12 x + 10 x

Collect like terms by calculating the sum or difference of their coefficients

(- 12 + 10) x

Add the numbers

- 2 x

- 7 x^{2} - 2 x + 32

- 7 x^{2} - 2 x + 32 = 0

Factor the expression

More Steps

Evaluate

- 7 x^{2} - 2 x + 32

Rewrite the expression

- 7 x^{2} + (- 16 + 14) x + 32

Calculate

- 7 x^{2} - 16 x + 14 x + 32

Rewrite the expression

- x \times 7 x - x \times 16 + 2 \times 7 x + 2 \times 16

Factor out - x from the expression

- x (7 x + 16) + 2 \times 7 x + 2 \times 16

Factor out 2 from the expression

- x (7 x + 16) + 2 (7 x + 16)

Factor out 7 x + 16 from the expression

(- x + 2) (7 x + 16)

(- x + 2) (7 x + 16) = 0

When the product of factors equals 0,at least one factor is 0

- x + 2 = 0 7 x + 16 = 0

Solve the equation for x

More Steps

Evaluate

- x + 2 = 0

Move the constant to the right-hand side and change its sign

- x = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

- x = - 2

Change the signs on both sides of the equation

x = 2

x = 2 7 x + 16 = 0

Solve the equation for x

More Steps

Evaluate

7 x + 16 = 0

Move the constant to the right-hand side and change its sign

7 x = 0 - 16

Removing 0 doesn't change the value,so remove it from the expression

7 x = - 16

Divide both sides

\frac{7 x}{7} = \frac{- 16}{7}

Divide the numbers

x = \frac{- 16}{7}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{16}{7}

x = 2 x = - \frac{16}{7}

Solution

x_{1} = - \frac{16}{7}, x_{2} = 2

Alternative Form

x_{1} = - 2. \dot{2} 8571 \dot{4}, x_{2} = 2

Show Solution