n^2-4n-25=7

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Solution for n^2-4n-25=7 equation:


Simplifying
n2 + -4n + -25 = 7

Reorder the terms:
-25 + -4n + n2 = 7

Solving
-25 + -4n + n2 = 7

Solving for variable 'n'.

Reorder the terms:
-25 + -7 + -4n + n2 = 7 + -7

Combine like terms: -25 + -7 = -32
-32 + -4n + n2 = 7 + -7

Combine like terms: 7 + -7 = 0
-32 + -4n + n2 = 0

Factor a trinomial.
(-4 + -1n)(8 + -1n) = 0

Subproblem 1

Set the factor '(-4 + -1n)' equal to zero and attempt to solve: Simplifying -4 + -1n = 0 Solving -4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = 0 + 4 -1n = 0 + 4 Combine like terms: 0 + 4 = 4 -1n = 4 Divide each side by '-1'. n = -4 Simplifying n = -4

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 = {-4, 8}

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