Solve 2y^2-y-6 - ScanMath

Question

Factor the expression

(y - 2) (2 y + 3)

Evaluate

2 y^{2} - y - 6

Rewrite the expression

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

Calculate

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

Rewrite the expression

y \times 2 y + y \times 3 - 2 \times 2 y - 2 \times 3

Factor out y from the expression

y (2 y + 3) - 2 \times 2 y - 2 \times 3

Factor out - 2 from the expression

y (2 y + 3) - 2 (2 y + 3)

Solution

(y - 2) (2 y + 3)

Show Solution

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

Alternative Form

y_{1} = - 1.5, y_{2} = 2

Evaluate

2 y^{2} - y - 6

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

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

Factor the expression

More Steps

Evaluate

2 y^{2} - y - 6

Rewrite the expression

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

Calculate

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

Rewrite the expression

y \times 2 y + y \times 3 - 2 \times 2 y - 2 \times 3

Factor out y from the expression

y (2 y + 3) - 2 \times 2 y - 2 \times 3

Factor out - 2 from the expression

y (2 y + 3) - 2 (2 y + 3)

Factor out 2 y + 3 from the expression

(y - 2) (2 y + 3)

(y - 2) (2 y + 3) = 0

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

y - 2 = 0 2 y + 3 = 0

Solve the equation for y

More Steps

Evaluate

y - 2 = 0

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

y = 0 + 2

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

y = 2

y = 2 2 y + 3 = 0

Solve the equation for y

More Steps

Evaluate

2 y + 3 = 0

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

2 y = 0 - 3

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

2 y = - 3

Divide both sides

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

Divide the numbers

y = \frac{- 3}{2}

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

y = - \frac{3}{2}

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

Solution

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

Alternative Form

y_{1} = - 1.5, y_{2} = 2

Show Solution