Solve 76/a=left(15-hright)^3+k

$$\frac{ 76 }{ a } = { \left(15-h \right) }^{ 3 } +k$$

Solve for a

$$a=\frac{76}{\left(15-h\right)^{3}+k}$$

$$h\neq \sqrt[3]{k}+15$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$76=a\left(15-h\right)^{3}+ak$$

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(15-h\right)^{3}.

$$76=a\left(3375-675h+45h^{2}-h^{3}\right)+ak$$

Use the distributive property to multiply a by 3375-675h+45h^{2}-h^{3}.

$$76=3375a-675ah+45ah^{2}-ah^{3}+ak$$

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

$$3375a-675ah+45ah^{2}-ah^{3}+ak=76$$

Combine all terms containing a.

$$\left(3375-675h+45h^{2}-h^{3}+k\right)a=76$$

The equation is in standard form.

$$\left(3375+k-675h+45h^{2}-h^{3}\right)a=76$$

Divide both sides by 3375-675h+45h^{2}-h^{3}+k.

$$\frac{\left(3375+k-675h+45h^{2}-h^{3}\right)a}{3375+k-675h+45h^{2}-h^{3}}=\frac{76}{3375+k-675h+45h^{2}-h^{3}}$$

Dividing by 3375-675h+45h^{2}-h^{3}+k undoes the multiplication by 3375-675h+45h^{2}-h^{3}+k.

$$a=\frac{76}{3375+k-675h+45h^{2}-h^{3}}$$

Variable a cannot be equal to 0.

$$a=\frac{76}{3375+k-675h+45h^{2}-h^{3}}\text{, }a\neq 0$$

Solve for h

$$h=-\sqrt[3]{-k+\frac{76}{a}}+15$$

$$a\neq 0$$