Solve 7 + y * (x + 2) ^ 3 = 2x(x ^ 2 - 2) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$7+y(x+2)^{3}=2x(x^{2}-2)$$

Solve for y

$y=-\frac{7+4x-2x^{3}}{\left(x+2\right)^{3}}$
$x\neq -2$

Steps for Solving Linear Equation

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

$$7+y\left(x^{3}+6x^{2}+12x+8\right)=2x\left(x^{2}-2\right)$$

Use the distributive property to multiply $y$ by $x^{3}+6x^{2}+12x+8$.

$$7+yx^{3}+6yx^{2}+12yx+8y=2x\left(x^{2}-2\right)$$

Use the distributive property to multiply $2x$ by $x^{2}-2$.

$$7+yx^{3}+6yx^{2}+12yx+8y=2x^{3}-4x$$

Subtract $7$ from both sides.

$$yx^{3}+6yx^{2}+12yx+8y=2x^{3}-4x-7$$

Combine all terms containing $y$.

$$\left(x^{3}+6x^{2}+12x+8\right)y=2x^{3}-4x-7$$

Divide both sides by $x^{3}+6x^{2}+12x+8$.

$$\frac{\left(x^{3}+6x^{2}+12x+8\right)y}{x^{3}+6x^{2}+12x+8}=\frac{2x^{3}-4x-7}{x^{3}+6x^{2}+12x+8}$$

Dividing by $x^{3}+6x^{2}+12x+8$ undoes the multiplication by $x^{3}+6x^{2}+12x+8$.

$$y=\frac{2x^{3}-4x-7}{x^{3}+6x^{2}+12x+8}$$

Divide $2x^{3}-4x-7$ by $x^{3}+6x^{2}+12x+8$.

$$y=\frac{2x^{3}-4x-7}{\left(x+2\right)^{3}}$$