n^2+3n=88

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Solution for n^2+3n=88 equation:


Simplifying
n2 + 3n = 88

Reorder the terms:
3n + n2 = 88

Solving
3n + n2 = 88

Solving for variable 'n'.

Reorder the terms:
-88 + 3n + n2 = 88 + -88

Combine like terms: 88 + -88 = 0
-88 + 3n + n2 = 0

Factor a trinomial.
(-11 + -1n)(8 + -1n) = 0

Subproblem 1

Set the factor '(-11 + -1n)' equal to zero and attempt to solve: Simplifying -11 + -1n = 0 Solving -11 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1n = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1n = 0 + 11 -1n = 0 + 11 Combine like terms: 0 + 11 = 11 -1n = 11 Divide each side by '-1'. n = -11 Simplifying n = -11

Subproblem 2

Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8

Solution

n = {-11, 8}

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