Solve 4y^2+12y+9/5div2y+3/10quadx=-4

$$\frac { 4 y ^ { 2 } + 12 y + 9 } { 5 } \div \frac { 2 y + 3 } { 10 } \quad x = - 4$$

Solve for x

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

$$y\neq -\frac{3}{2}$$

Steps for Solving Linear Equation

Divide \frac{4y^{2}+12y+9}{5} by \frac{2y+3}{10} by multiplying \frac{4y^{2}+12y+9}{5} by the reciprocal of \frac{2y+3}{10}.

$$\frac{\left(4y^{2}+12y+9\right)\times 10}{5\left(2y+3\right)}x=-4$$

Cancel out 5 in both numerator and denominator.

$$\frac{2\left(4y^{2}+12y+9\right)}{2y+3}x=-4$$

Factor the expressions that are not already factored in \frac{2\left(4y^{2}+12y+9\right)}{2y+3}.

$$\frac{2\left(2y+3\right)^{2}}{2y+3}x=-4$$

Cancel out 2y+3 in both numerator and denominator.

$$2\left(2y+3\right)x=-4$$

Expand the expression.

$$\left(4y+6\right)x=-4$$

Divide both sides by 6+4y.

$$\frac{\left(4y+6\right)x}{4y+6}=-\frac{4}{4y+6}$$

Dividing by 6+4y undoes the multiplication by 6+4y.

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

Divide -4 by 6+4y.

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

Solve for y

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

$$x\neq 0$$