Solve 3y^(2)-6=-7y

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

y_{1} = - 3, y_{2} = 0. \dot{6}

Evaluate

3 y^{2} - 6 = - 7 y

Move the expression to the left side

3 y^{2} - 6 + 7 y = 0

Factor the expression

More Steps

Evaluate

3 y^{2} - 6 + 7 y

Reorder the terms

3 y^{2} + 7 y - 6

Rewrite the expression

3 y^{2} + (- 2 + 9) y - 6

Calculate

3 y^{2} - 2 y + 9 y - 6

Rewrite the expression

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

Factor out y from the expression

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

Factor out 3 from the expression

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

Factor out 3 y - 2 from the expression

(y + 3) (3 y - 2)

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

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

3 y - 2 = 0 y + 3 = 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}

y = \frac{2}{3} y + 3 = 0

Solve the equation for y

More Steps

Evaluate

y + 3 = 0

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

y = 0 - 3

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

y = - 3

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

Solution

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

Alternative Form

y_{1} = - 3, y_{2} = 0. \dot{6}

Show Solution