Solve 6x^2-x-12 - ScanMath

Question

Factor the expression

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

Evaluate

6 x^{2} - x - 12

Rewrite the expression

6 x^{2} + (8 - 9) x - 12

Calculate

6 x^{2} + 8 x - 9 x - 12

Rewrite the expression

2 x \times 3 x + 2 x \times 4 - 3 \times 3 x - 3 \times 4

Factor out 2 x from the expression

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

Factor out - 3 from the expression

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

Solution

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

Show Solution

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

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 1.5

Evaluate

6 x^{2} - x - 12

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

6 x^{2} - x - 12 = 0

Factor the expression

More Steps

Evaluate

6 x^{2} - x - 12

Rewrite the expression

6 x^{2} + (8 - 9) x - 12

Calculate

6 x^{2} + 8 x - 9 x - 12

Rewrite the expression

2 x \times 3 x + 2 x \times 4 - 3 \times 3 x - 3 \times 4

Factor out 2 x from the expression

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

Factor out - 3 from the expression

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

Factor out 3 x + 4 from the expression

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

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

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

2 x - 3 = 0 3 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 3 = 0

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

2 x = 0 + 3

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

2 x = 3

Divide both sides

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

Divide the numbers

x = \frac{3}{2}

x = \frac{3}{2} 3 x + 4 = 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}

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

x = - \frac{4}{3}

x = \frac{3}{2} x = - \frac{4}{3}

Solution

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

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 1.5

Show Solution