Solve (x-3)(5x+12)

Question

Simplify the expression

5 x^{2} - 3 x - 36

Evaluate

(x - 3) (5 x + 12)

Apply the distributive property

x \times 5 x + x \times 12 - 3 \times 5 x - 3 \times 12

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}

5 x^{2} + x \times 12 - 3 \times 5 x - 3 \times 12

Use the commutative property to reorder the terms

5 x^{2} + 12 x - 3 \times 5 x - 3 \times 12

Multiply the numbers

5 x^{2} + 12 x - 15 x - 3 \times 12

Multiply the numbers

5 x^{2} + 12 x - 15 x - 36

Solution

More Steps

Evaluate

12 x - 15 x

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

(12 - 15) x

Subtract the numbers

- 3 x

5 x^{2} - 3 x - 36

Show Solution

x_{1} = - \frac{12}{5}, x_{2} = 3

Alternative Form

x_{1} = - 2.4, x_{2} = 3

Evaluate

(x - 3) (5 x + 12)

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

(x - 3) (5 x + 12) = 0

Separate the equation into 2 possible cases

x - 3 = 0 5 x + 12 = 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 5 x + 12 = 0

Solve the equation

More Steps

Evaluate

5 x + 12 = 0

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

5 x = 0 - 12

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

5 x = - 12

Divide both sides

\frac{5 x}{5} = \frac{- 12}{5}

Divide the numbers

x = \frac{- 12}{5}

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

x = - \frac{12}{5}

x = 3 x = - \frac{12}{5}

Solution

x_{1} = - \frac{12}{5}, x_{2} = 3

Alternative Form

x_{1} = - 2.4, x_{2} = 3

Show Solution