Solve 5(x-4) (2x-7)

Question

Simplify the expression

10 x^{2} - 75 x + 140

Evaluate

5 (x - 4) (2 x - 7)

Multiply the terms

More Steps

Evaluate

5 (x - 4)

Apply the distributive property

5 x - 5 \times 4

Multiply the numbers

5 x - 20

(5 x - 20) (2 x - 7)

Apply the distributive property

5 x \times 2 x - 5 x \times 7 - 20 \times 2 x - (- 20 \times 7)

Multiply the terms

More Steps

Evaluate

5 x \times 2 x

Multiply the numbers

10 x \times x

Multiply the terms

10 x^{2}

10 x^{2} - 5 x \times 7 - 20 \times 2 x - (- 20 \times 7)

Multiply the numbers

10 x^{2} - 35 x - 20 \times 2 x - (- 20 \times 7)

Multiply the numbers

10 x^{2} - 35 x - 40 x - (- 20 \times 7)

Multiply the numbers

10 x^{2} - 35 x - 40 x - (- 140)

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

10 x^{2} - 35 x - 40 x + 140

Solution

More Steps

Evaluate

- 35 x - 40 x

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

(- 35 - 40) x

Subtract the numbers

- 75 x

10 x^{2} - 75 x + 140

Show Solution

Find the roots

x_{1} = \frac{7}{2}, x_{2} = 4

Alternative Form

x_{1} = 3.5, x_{2} = 4

Evaluate

5 (x - 4) (2 x - 7)

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

5 (x - 4) (2 x - 7) = 0

Elimination the left coefficient

(x - 4) (2 x - 7) = 0

Separate the equation into 2 possible cases

x - 4 = 0 2 x - 7 = 0

Solve the equation

More Steps

Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = 4 2 x - 7 = 0

Solve the equation

More Steps

Evaluate

2 x - 7 = 0

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

2 x = 0 + 7

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

2 x = 7

Divide both sides

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

Divide the numbers

x = \frac{7}{2}

x = 4 x = \frac{7}{2}

Solution

x_{1} = \frac{7}{2}, x_{2} = 4

Alternative Form

x_{1} = 3.5, x_{2} = 4

Show Solution