Solve (40-2x)(26-x)=144xb

$$( 40 - 2 x ) ( 26 - x ) = 144 x b$$

Solve for b

$$b=\frac{x}{72}-\frac{23}{36}+\frac{65}{9x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 40-2x by 26-x and combine like terms.

$$1040-92x+2x^{2}=144xb$$

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

$$144xb=1040-92x+2x^{2}$$

The equation is in standard form.

$$144xb=2x^{2}-92x+1040$$

Divide both sides by 144x.

$$\frac{144xb}{144x}=\frac{2\left(x-26\right)\left(x-20\right)}{144x}$$

Dividing by 144x undoes the multiplication by 144x.

$$b=\frac{2\left(x-26\right)\left(x-20\right)}{144x}$$

Divide 2\left(-26+x\right)\left(-20+x\right) by 144x.

$$b=\frac{x}{72}-\frac{23}{36}+\frac{65}{9x}$$

Solve for x (complex solution)

$$x=3\sqrt{144b^{2}+184b+1}+36b+23$$

$$x=-3\sqrt{144b^{2}+184b+1}+36b+23$$

Solve for x

$$x=3\sqrt{144b^{2}+184b+1}+36b+23$$

$$x=-3\sqrt{144b^{2}+184b+1}+36b+23\text{, }b\geq \frac{\sqrt{130}}{18}-\frac{23}{36}\text{ or }b\leq -\frac{\sqrt{130}}{18}-\frac{23}{36}$$