Solve w=tx^2+x(30-2t)

$$w = t x ^ { 2 } + x ( 30 - 2 t )$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=\frac{w-30x}{x\left(x-2\right)}\text{, }&x\neq 2\text{ and }x\neq 0\\t\in \mathrm{C}\text{, }&\left(w=0\text{ and }x=0\right)\text{ or }\left(w=60\text{ and }x=2\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 30-2t.

$$w=tx^{2}+30x-2xt$$

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

$$tx^{2}+30x-2xt=w$$

Subtract 30x from both sides.

$$tx^{2}-2xt=w-30x$$

Combine all terms containing t.

$$\left(x^{2}-2x\right)t=w-30x$$

Divide both sides by x^{2}-2x.

$$\frac{\left(x^{2}-2x\right)t}{x^{2}-2x}=\frac{w-30x}{x^{2}-2x}$$

Dividing by x^{2}-2x undoes the multiplication by x^{2}-2x.

$$t=\frac{w-30x}{x^{2}-2x}$$

Divide -30x+w by x^{2}-2x.

$$t=\frac{w-30x}{x\left(x-2\right)}$$

Solve for t

$$\left\{\begin{matrix}t=\frac{w-30x}{x\left(x-2\right)}\text{, }&x\neq 2\text{ and }x\neq 0\\t\in \mathrm{R}\text{, }&\left(w=0\text{ and }x=0\right)\text{ or }\left(w=60\text{ and }x=2\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 30-2t.

$$w=tx^{2}+30x-2xt$$

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

$$tx^{2}+30x-2xt=w$$

Subtract 30x from both sides.

$$tx^{2}-2xt=w-30x$$

Combine all terms containing t.

$$\left(x^{2}-2x\right)t=w-30x$$

Divide both sides by x^{2}-2x.

$$\frac{\left(x^{2}-2x\right)t}{x^{2}-2x}=\frac{w-30x}{x^{2}-2x}$$

Dividing by x^{2}-2x undoes the multiplication by x^{2}-2x.

$$t=\frac{w-30x}{x^{2}-2x}$$

Divide -30x+w by x^{2}-2x.

$$t=\frac{w-30x}{x\left(x-2\right)}$$

Solve for w

$$w=x\left(tx-2t+30\right)$$