Solve 3x^2-16x-12

Question

Factor the expression

(x - 6) (3 x + 2)

Evaluate

3 x^{2} - 16 x - 12

Rewrite the expression

3 x^{2} + (2 - 18) x - 12

Calculate

3 x^{2} + 2 x - 18 x - 12

Rewrite the expression

x \times 3 x + x \times 2 - 6 \times 3 x - 6 \times 2

Factor out x from the expression

x (3 x + 2) - 6 \times 3 x - 6 \times 2

Factor out - 6 from the expression

x (3 x + 2) - 6 (3 x + 2)

Solution

(x - 6) (3 x + 2)

Show Solution

x_{1} = - \frac{2}{3}, x_{2} = 6

Alternative Form

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

Evaluate

3 x^{2} - 16 x - 12

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

3 x^{2} - 16 x - 12 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 16 x - 12

Rewrite the expression

3 x^{2} + (2 - 18) x - 12

Calculate

3 x^{2} + 2 x - 18 x - 12

Rewrite the expression

x \times 3 x + x \times 2 - 6 \times 3 x - 6 \times 2

Factor out x from the expression

x (3 x + 2) - 6 \times 3 x - 6 \times 2

Factor out - 6 from the expression

x (3 x + 2) - 6 (3 x + 2)

Factor out 3 x + 2 from the expression

(x - 6) (3 x + 2)

(x - 6) (3 x + 2) = 0

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

x - 6 = 0 3 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

x - 6 = 0

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

x = 0 + 6

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

x = 6

x = 6 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 = 6 x = - \frac{2}{3}

Solution

x_{1} = - \frac{2}{3}, x_{2} = 6

Alternative Form

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

Show Solution