Solve 15x^2-11x-12

Question

Factor the expression

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

Evaluate

15 x^{2} - 11 x - 12

Rewrite the expression

15 x^{2} + (9 - 20) x - 12

Calculate

15 x^{2} + 9 x - 20 x - 12

Rewrite the expression

3 x \times 5 x + 3 x \times 3 - 4 \times 5 x - 4 \times 3

Factor out 3 x from the expression

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

Factor out - 4 from the expression

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

Solution

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

Show Solution

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

Alternative Form

x_{1} = - 0.6, x_{2} = 1. \dot{3}

Evaluate

15 x^{2} - 11 x - 12

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

15 x^{2} - 11 x - 12 = 0

Factor the expression

More Steps

Evaluate

15 x^{2} - 11 x - 12

Rewrite the expression

15 x^{2} + (9 - 20) x - 12

Calculate

15 x^{2} + 9 x - 20 x - 12

Rewrite the expression

3 x \times 5 x + 3 x \times 3 - 4 \times 5 x - 4 \times 3

Factor out 3 x from the expression

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

Factor out - 4 from the expression

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

Factor out 5 x + 3 from the expression

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

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

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

3 x - 4 = 0 5 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 4 = 0

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

3 x = 0 + 4

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

3 x = 4

Divide both sides

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

Divide the numbers

x = \frac{4}{3}

x = \frac{4}{3} 5 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

5 x + 3 = 0

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

5 x = 0 - 3

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

5 x = - 3

Divide both sides

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

Divide the numbers

x = \frac{- 3}{5}

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

x = - \frac{3}{5}

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

Solution

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

Alternative Form

x_{1} = - 0.6, x_{2} = 1. \dot{3}

Show Solution