Solve for y 4x^2+6x-2y=10

$4 x^{2} + 6 x - 2 y = 10$

Move all terms not containing $y$ to the right side of the equation.

Subtract $4 x^{2}$ from both sides of the equation.

$6 x - 2 y = 10 - 4 x^{2}$

Subtract $6 x$ from both sides of the equation.

$- 2 y = 10 - 4 x^{2} - 6 x$

Divide each term in $- 2 y = 10 - 4 x^{2} - 6 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 10 - 4 x^{2} - 6 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{10}{- 2} + \frac{- 4 x^{2}}{- 2} + \frac{- 6 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{10}{- 2} + \frac{- 4 x^{2}}{- 2} + \frac{- 6 x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{10}{- 2} + \frac{- 4 x^{2}}{- 2} + \frac{- 6 x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $10$ by $- 2$ .

$y = - 5 + \frac{- 4 x^{2}}{- 2} + \frac{- 6 x}{- 2}$

Cancel the common factor of $- 4$ and $- 2$ .

Factor $- 2$ out of $- 4 x^{2}$ .

$y = - 5 + \frac{- 2 (2 x^{2})}{- 2} + \frac{- 6 x}{- 2}$

Cancel the common factors.

Factor $- 2$ out of $- 2$ .

$y = - 5 + \frac{- 2 (2 x^{2})}{- 2 (1)} + \frac{- 6 x}{- 2}$

Cancel the common factor.

$y = - 5 + \frac{- 2 (2 x^{2})}{- 2 \cdot 1} + \frac{- 6 x}{- 2}$

Rewrite the expression.

$y = - 5 + \frac{2 x^{2}}{1} + \frac{- 6 x}{- 2}$

Divide $2 x^{2}$ by $1$ .

$y = - 5 + 2 x^{2} + \frac{- 6 x}{- 2}$

Cancel the common factor of $- 6$ and $- 2$ .

Factor $- 2$ out of $- 6 x$ .

$y = - 5 + 2 x^{2} + \frac{- 2 (3 x)}{- 2}$

Cancel the common factors.

Factor $- 2$ out of $- 2$ .

$y = - 5 + 2 x^{2} + \frac{- 2 (3 x)}{- 2 (1)}$

Cancel the common factor.

$y = - 5 + 2 x^{2} + \frac{- 2 (3 x)}{- 2 \cdot 1}$

Rewrite the expression.

$y = - 5 + 2 x^{2} + \frac{3 x}{1}$

Divide $3 x$ by $1$ .

$y = - 5 + 2 x^{2} + 3 x$