Solve 3y^2-4y-4 - ScanMath

Question

Factor the expression

(y - 2) (3 y + 2)

Evaluate

3 y^{2} - 4 y - 4

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out y from the expression

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

Factor out - 2 from the expression

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

Solution

(y - 2) (3 y + 2)

Show Solution

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

Alternative Form

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

Evaluate

3 y^{2} - 4 y - 4

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

3 y^{2} - 4 y - 4 = 0

Factor the expression

More Steps

Evaluate

3 y^{2} - 4 y - 4

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out y from the expression

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

Factor out - 2 from the expression

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

Factor out 3 y + 2 from the expression

(y - 2) (3 y + 2)

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

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

y - 2 = 0 3 y + 2 = 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 3 y + 2 = 0

Solve the equation for y

More Steps

Evaluate

3 y + 2 = 0

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

3 y = 0 - 2

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

3 y = - 2

Divide both sides

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

Divide the numbers

y = \frac{- 2}{3}

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

y = - \frac{2}{3}

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

Solution

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

Alternative Form

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

Show Solution