Solve y=a/x-3+10(x-6)^2

$$y = \frac { a } { x - 3 } + 10 ( x - 6 ) ^ { 2 }$$

Solve for a

$$a=-\left(3-x\right)\left(-10\left(x-6\right)^{2}+y\right)$$

$$x\neq 3$$

Solution Steps

Multiply both sides of the equation by x-3.

$$y\left(x-3\right)=a+10\left(x-6\right)^{2}\left(x-3\right)$$

Use the distributive property to multiply y by x-3.

$$yx-3y=a+10\left(x-6\right)^{2}\left(x-3\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$yx-3y=a+10\left(x^{2}-12x+36\right)\left(x-3\right)$$

Use the distributive property to multiply 10 by x^{2}-12x+36.

$$yx-3y=a+\left(10x^{2}-120x+360\right)\left(x-3\right)$$

Use the distributive property to multiply 10x^{2}-120x+360 by x-3 and combine like terms.

$$yx-3y=a+10x^{3}-150x^{2}+720x-1080$$

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

$$a+10x^{3}-150x^{2}+720x-1080=yx-3y$$

Subtract 10x^{3} from both sides.

$$a-150x^{2}+720x-1080=yx-3y-10x^{3}$$

Add 150x^{2} to both sides.

$$a+720x-1080=yx-3y-10x^{3}+150x^{2}$$

Subtract 720x from both sides.

$$a-1080=yx-3y-10x^{3}+150x^{2}-720x$$

Add 1080 to both sides.

$$a=yx-3y-10x^{3}+150x^{2}-720x+1080$$