Solve 9x^2-39x-30

Question

Factor the expression

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

Evaluate

9 x^{2} - 39 x - 30

Rewrite the expression

3 \times 3 x^{2} - 3 \times 13 x - 3 \times 10

Factor out 3 from the expression

3 (3 x^{2} - 13 x - 10)

Solution

More Steps

Evaluate

3 x^{2} - 13 x - 10

Rewrite the expression

3 x^{2} + (2 - 15) x - 10

Calculate

3 x^{2} + 2 x - 15 x - 10

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 5 from the expression

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

Factor out 3 x + 2 from the expression

(x - 5) (3 x + 2)

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

Show Solution

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 5

Evaluate

9 x^{2} - 39 x - 30

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

9 x^{2} - 39 x - 30 = 0

Factor the expression

More Steps

Evaluate

9 x^{2} - 39 x - 30

Rewrite the expression

3 \times 3 x^{2} - 3 \times 13 x - 3 \times 10

Factor out 3 from the expression

3 (3 x^{2} - 13 x - 10)

Factor the expression

More Steps

Evaluate

3 x^{2} - 13 x - 10

Rewrite the expression

3 x^{2} + (2 - 15) x - 10

Calculate

3 x^{2} + 2 x - 15 x - 10

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 5 from the expression

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

Factor out 3 x + 2 from the expression

(x - 5) (3 x + 2)

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

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

Divide the terms

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

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

x - 5 = 0 3 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 5 3 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 2 = 0

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

3 x = 0 - 2

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

3 x = - 2

Divide both sides

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

Divide the numbers

x = \frac{- 2}{3}

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

x = - \frac{2}{3}

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

Solution

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 5

Show Solution