Solve 12x^2+2x-2 - ScanMath

Question

Factor the expression

Factor

2 (2 x + 1) (3 x - 1)

Evaluate

12 x^{2} + 2 x - 2

Rewrite the expression

2 \times 6 x^{2} + 2 x - 2

Factor out 2 from the expression

2 (6 x^{2} + x - 1)

Solution

More Steps

Evaluate

6 x^{2} + x - 1

Rewrite the expression

6 x^{2} + (- 2 + 3) x - 1

Calculate

6 x^{2} - 2 x + 3 x - 1

Rewrite the expression

2 x \times 3 x - 2 x + 3 x - 1

Factor out 2 x from the expression

2 x (3 x - 1) + 3 x - 1

Factor out 3 x - 1 from the expression

(2 x + 1) (3 x - 1)

2 (2 x + 1) (3 x - 1)

Show Solution

Find the roots

Find the roots of the algebra expression

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

Alternative Form

x_{1} = - 0.5, x_{2} = 0. \dot{3}

Evaluate

12 x^{2} + 2 x - 2

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

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

Factor the expression

More Steps

Evaluate

12 x^{2} + 2 x - 2

Rewrite the expression

2 \times 6 x^{2} + 2 x - 2

Factor out 2 from the expression

2 (6 x^{2} + x - 1)

Factor the expression

More Steps

Evaluate

6 x^{2} + x - 1

Rewrite the expression

6 x^{2} + (- 2 + 3) x - 1

Calculate

6 x^{2} - 2 x + 3 x - 1

Rewrite the expression

2 x \times 3 x - 2 x + 3 x - 1

Factor out 2 x from the expression

2 x (3 x - 1) + 3 x - 1

Factor out 3 x - 1 from the expression

(2 x + 1) (3 x - 1)

2 (2 x + 1) (3 x - 1)

2 (2 x + 1) (3 x - 1) = 0

Divide the terms

(2 x + 1) (3 x - 1) = 0

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

2 x + 1 = 0 3 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 1 = 0

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

2 x = 0 - 1

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

2 x = - 1

Divide both sides

\frac{2 x}{2} = \frac{- 1}{2}

Divide the numbers

x = \frac{- 1}{2}

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

x = - \frac{1}{2}

x = - \frac{1}{2} 3 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 1 = 0

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

3 x = 0 + 1

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

3 x = 1

Divide both sides

\frac{3 x}{3} = \frac{1}{3}

Divide the numbers

x = \frac{1}{3}

x = - \frac{1}{2} x = \frac{1}{3}

Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 0. \dot{3}

Show Solution

12x^2+2x 2

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression