Solve 6x^2-x-2 - ScanMath

Question

Factor the expression

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

Evaluate

6 x^{2} - x - 2

Rewrite the expression

6 x^{2} + (- 4 + 3) x - 2

Calculate

6 x^{2} - 4 x + 3 x - 2

Rewrite the expression

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

Factor out 2 x from the expression

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

Solution

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

Show Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 0. \dot{6}

Evaluate

6 x^{2} - x - 2

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

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

Factor the expression

More Steps

Evaluate

6 x^{2} - x - 2

Rewrite the expression

6 x^{2} + (- 4 + 3) x - 2

Calculate

6 x^{2} - 4 x + 3 x - 2

Rewrite the expression

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

Factor out 2 x from the expression

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

Factor out 3 x - 2 from the expression

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

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

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

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

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

Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 0. \dot{6}

Show Solution