Solve (x-3)*(4-5x)

Question

Simplify the expression

19 x - 5 x^{2} - 12

Evaluate

(x - 3) (4 - 5 x)

Apply the distributive property

x \times 4 - x \times 5 x - 3 \times 4 - (- 3 \times 5 x)

Use the commutative property to reorder the terms

4 x - x \times 5 x - 3 \times 4 - (- 3 \times 5 x)

Multiply the terms

More Steps

Evaluate

x \times 5 x

Use the commutative property to reorder the terms

5 x \times x

Multiply the terms

5 x^{2}

4 x - 5 x^{2} - 3 \times 4 - (- 3 \times 5 x)

Multiply the numbers

4 x - 5 x^{2} - 12 - (- 3 \times 5 x)

Multiply the numbers

4 x - 5 x^{2} - 12 - (- 15 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

4 x - 5 x^{2} - 12 + 15 x

Solution

More Steps

Evaluate

4 x + 15 x

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

(4 + 15) x

Add the numbers

19 x

19 x - 5 x^{2} - 12

Show Solution

Find the roots

x_{1} = \frac{4}{5}, x_{2} = 3

Alternative Form

x_{1} = 0.8, x_{2} = 3

Evaluate

(x - 3) (4 - 5 x)

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

(x - 3) (4 - 5 x) = 0

Separate the equation into 2 possible cases

x - 3 = 0 4 - 5 x = 0

Solve the equation

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 4 - 5 x = 0

Solve the equation

More Steps

Evaluate

4 - 5 x = 0

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

- 5 x = 0 - 4

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

- 5 x = - 4

Change the signs on both sides of the equation

5 x = 4

Divide both sides

\frac{5 x}{5} = \frac{4}{5}

Divide the numbers

x = \frac{4}{5}

x = 3 x = \frac{4}{5}

Solution

x_{1} = \frac{4}{5}, x_{2} = 3

Alternative Form

x_{1} = 0.8, x_{2} = 3

Show Solution