Solve (2x+1)(9x+2m)-5(x+2)=40

$$( 2 x + 1 ) ( 9 x + 2 m ) - 5 ( x + 2 ) = 40$$

Solve for m

$$m=-\frac{9x^{2}+2x-25}{2x+1}$$

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

Steps for Solving Linear Equation

Use the distributive property to multiply 2x+1 by 9x+2m.

$$18x^{2}+4mx+9x+2m-5\left(x+2\right)=40$$

Use the distributive property to multiply -5 by x+2.

$$18x^{2}+4mx+9x+2m-5x-10=40$$

Combine 9x and -5x to get 4x.

$$18x^{2}+4mx+4x+2m-10=40$$

Subtract 18x^{2} from both sides.

$$4mx+4x+2m-10=40-18x^{2}$$

Subtract 4x from both sides.

$$4mx+2m-10=40-18x^{2}-4x$$

Add 10 to both sides.

$$4mx+2m=40-18x^{2}-4x+10$$

Add 40 and 10 to get 50.

$$4mx+2m=50-18x^{2}-4x$$

Combine all terms containing m.

$$\left(4x+2\right)m=50-18x^{2}-4x$$

The equation is in standard form.

$$\left(4x+2\right)m=50-4x-18x^{2}$$

Divide both sides by 4x+2.

$$\frac{\left(4x+2\right)m}{4x+2}=\frac{50-4x-18x^{2}}{4x+2}$$

Dividing by 4x+2 undoes the multiplication by 4x+2.

$$m=\frac{50-4x-18x^{2}}{4x+2}$$

Divide 50-18x^{2}-4x by 4x+2.

$$m=\frac{25-2x-9x^{2}}{2x+1}$$

Solve for x

$$x=\frac{\sqrt{m^{2}-7m+226}-m-1}{9}$$

$$x=\frac{-\sqrt{m^{2}-7m+226}-m-1}{9}$$