Solve (x-4)(5x+6)

Question

Simplify the expression

5 x^{2} - 14 x - 24

Evaluate

(x - 4) (5 x + 6)

Apply the distributive property

x \times 5 x + x \times 6 - 4 \times 5 x - 4 \times 6

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 6 - 4 \times 5 x - 4 \times 6

Use the commutative property to reorder the terms

5 x^{2} + 6 x - 4 \times 5 x - 4 \times 6

Multiply the numbers

5 x^{2} + 6 x - 20 x - 4 \times 6

Multiply the numbers

5 x^{2} + 6 x - 20 x - 24

Solution

More Steps

Evaluate

6 x - 20 x

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

(6 - 20) x

Subtract the numbers

- 14 x

5 x^{2} - 14 x - 24

Show Solution

x_{1} = - \frac{6}{5}, x_{2} = 4

Alternative Form

x_{1} = - 1.2, x_{2} = 4

Evaluate

(x - 4) (5 x + 6)

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

(x - 4) (5 x + 6) = 0

Separate the equation into 2 possible cases

x - 4 = 0 5 x + 6 = 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 5 x + 6 = 0

Solve the equation

More Steps

Evaluate

5 x + 6 = 0

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

5 x = 0 - 6

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

5 x = - 6

Divide both sides

\frac{5 x}{5} = \frac{- 6}{5}

Divide the numbers

x = \frac{- 6}{5}

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

x = - \frac{6}{5}

x = 4 x = - \frac{6}{5}

Solution

x_{1} = - \frac{6}{5}, x_{2} = 4

Alternative Form

x_{1} = - 1.2, x_{2} = 4

Show Solution