Solve 2x^2+3x=(2x-1)(x+m

$$2 x ^ { 2 } + 3 x = ( 2 x - 1 ) ( x + m$$

Solve for m

$$m=-\frac{4x}{1-2x}$$

$$x\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-1 by x+m.

$$2x^{2}+3x=2x^{2}+2xm-x-m$$

Swap sides so that all variable terms are on the left hand side.

$$2x^{2}+2xm-x-m=2x^{2}+3x$$

Subtract 2x^{2} from both sides.

$$2xm-x-m=2x^{2}+3x-2x^{2}$$

Combine 2x^{2} and -2x^{2} to get 0.

$$2xm-x-m=3x$$

Add x to both sides.

$$2xm-m=3x+x$$

Combine 3x and x to get 4x.

$$2xm-m=4x$$

Combine all terms containing m.

$$\left(2x-1\right)m=4x$$

Divide both sides by 2x-1.

$$\frac{\left(2x-1\right)m}{2x-1}=\frac{4x}{2x-1}$$

Dividing by 2x-1 undoes the multiplication by 2x-1.

$$m=\frac{4x}{2x-1}$$

Solve for x

$$x=-\frac{m}{2\left(2-m\right)}$$

$$m\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-1 by x+m.

$$2x^{2}+3x=2x^{2}+2xm-x-m$$

Subtract 2x^{2} from both sides.

$$2x^{2}+3x-2x^{2}=2xm-x-m$$

Combine 2x^{2} and -2x^{2} to get 0.

$$3x=2xm-x-m$$

Subtract 2xm from both sides.

$$3x-2xm=-x-m$$

Add x to both sides.

$$3x-2xm+x=-m$$

Combine 3x and x to get 4x.

$$4x-2xm=-m$$

Combine all terms containing x.

$$\left(4-2m\right)x=-m$$

Divide both sides by 4-2m.

$$\frac{\left(4-2m\right)x}{4-2m}=-\frac{m}{4-2m}$$

Dividing by 4-2m undoes the multiplication by 4-2m.

$$x=-\frac{m}{4-2m}$$

Divide -m by 4-2m.

$$x=-\frac{m}{2\left(2-m\right)}$$