Solve 20x^2-52x-24

Question

Factor the expression

4 (x - 3) (5 x + 2)

Evaluate

20 x^{2} - 52 x - 24

Rewrite the expression

4 \times 5 x^{2} - 4 \times 13 x - 4 \times 6

Factor out 4 from the expression

4 (5 x^{2} - 13 x - 6)

Solution

More Steps

Evaluate

5 x^{2} - 13 x - 6

Rewrite the expression

5 x^{2} + (2 - 15) x - 6

Calculate

5 x^{2} + 2 x - 15 x - 6

Rewrite the expression

x \times 5 x + x \times 2 - 3 \times 5 x - 3 \times 2

Factor out x from the expression

x (5 x + 2) - 3 \times 5 x - 3 \times 2

Factor out - 3 from the expression

x (5 x + 2) - 3 (5 x + 2)

Factor out 5 x + 2 from the expression

(x - 3) (5 x + 2)

4 (x - 3) (5 x + 2)

Show Solution

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

Alternative Form

x_{1} = - 0.4, x_{2} = 3

Evaluate

20 x^{2} - 52 x - 24

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

20 x^{2} - 52 x - 24 = 0

Factor the expression

More Steps

Evaluate

20 x^{2} - 52 x - 24

Rewrite the expression

4 \times 5 x^{2} - 4 \times 13 x - 4 \times 6

Factor out 4 from the expression

4 (5 x^{2} - 13 x - 6)

Factor the expression

More Steps

Evaluate

5 x^{2} - 13 x - 6

Rewrite the expression

5 x^{2} + (2 - 15) x - 6

Calculate

5 x^{2} + 2 x - 15 x - 6

Rewrite the expression

x \times 5 x + x \times 2 - 3 \times 5 x - 3 \times 2

Factor out x from the expression

x (5 x + 2) - 3 \times 5 x - 3 \times 2

Factor out - 3 from the expression

x (5 x + 2) - 3 (5 x + 2)

Factor out 5 x + 2 from the expression

(x - 3) (5 x + 2)

4 (x - 3) (5 x + 2)

4 (x - 3) (5 x + 2) = 0

Divide the terms

(x - 3) (5 x + 2) = 0

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

x - 3 = 0 5 x + 2 = 0

Solve the equation for x

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 + 2 = 0

Solve the equation for x

More Steps

Evaluate

5 x + 2 = 0

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

5 x = 0 - 2

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

5 x = - 2

Divide both sides

\frac{5 x}{5} = \frac{- 2}{5}

Divide the numbers

x = \frac{- 2}{5}

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

x = - \frac{2}{5}

x = 3 x = - \frac{2}{5}

Solution

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

Alternative Form

x_{1} = - 0.4, x_{2} = 3

Show Solution