Solve (n + 12)(n + 3) = n(n + 9) + 84 | 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

$$(n+12)(n+3)=n(n+9)+84.$$

Solve for n

$n=8$

Steps for Solving Linear Equation

Use the distributive property to multiply $n+12$ by $n+3$ and combine like terms.

$$n^{2}+15n+36=n\left(n+9\right)+84$$

Use the distributive property to multiply $n$ by $n+9$.

$$n^{2}+15n+36=n^{2}+9n+84$$

Subtract $n^{2}$ from both sides.

$$n^{2}+15n+36-n^{2}=9n+84$$

Combine $n^{2}$ and $-n^{2}$ to get $0$.

$$15n+36=9n+84$$

Subtract $9n$ from both sides.

$$15n+36-9n=84$$

Combine $15n$ and $-9n$ to get $6n$.

$$6n+36=84$$

Subtract $36$ from both sides.

$$6n=84-36$$

Subtract $36$ from $84$ to get $48$.

$$6n=48$$

Divide both sides by $6$.

$$n=\frac{48}{6}$$

Divide $48$ by $6$ to get $8$.

$$n=8$$