-7n^2+4n-23=-10n^2-8

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Solution for -7n^2+4n-23=-10n^2-8 equation: 


Simplifying
-7n2 + 4n + -23 = -10n2 + -8

Reorder the terms:
-23 + 4n + -7n2 = -10n2 + -8

Reorder the terms:
-23 + 4n + -7n2 = -8 + -10n2

Solving
-23 + 4n + -7n2 = -8 + -10n2

Solving for variable 'n'.

Reorder the terms:
-23 + 8 + 4n + -7n2 + 10n2 = -8 + -10n2 + 8 + 10n2

Combine like terms: -23 + 8 = -15
-15 + 4n + -7n2 + 10n2 = -8 + -10n2 + 8 + 10n2

Combine like terms: -7n2 + 10n2 = 3n2
-15 + 4n + 3n2 = -8 + -10n2 + 8 + 10n2

Reorder the terms:
-15 + 4n + 3n2 = -8 + 8 + -10n2 + 10n2

Combine like terms: -8 + 8 = 0
-15 + 4n + 3n2 = 0 + -10n2 + 10n2
-15 + 4n + 3n2 = -10n2 + 10n2

Combine like terms: -10n2 + 10n2 = 0
-15 + 4n + 3n2 = 0

Factor a trinomial.
(-3 + -1n)(5 + -3n) = 0


Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3

Subproblem 2
Set the factor '(5 + -3n)' equal to zero and attempt to solve:

Simplifying
5 + -3n = 0

Solving
5 + -3n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3n = 0 + -5
-3n = 0 + -5

Combine like terms: 0 + -5 = -5
-3n = -5

Divide each side by '-3'.
n = 1.666666667

Simplifying
n = 1.666666667
Solution
n = {-3, 1.666666667}

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