-90+5x^2-4x=2x^2-1x-30

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Solution for -90+5x^2-4x=2x^2-1x-30 equation: 


Simplifying
-90 + 5x2 + -4x = 2x2 + -1x + -30

Reorder the terms:
-90 + -4x + 5x2 = 2x2 + -1x + -30

Reorder the terms:
-90 + -4x + 5x2 = -30 + -1x + 2x2

Solving
-90 + -4x + 5x2 = -30 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-90 + 30 + -4x + x + 5x2 + -2x2 = -30 + -1x + 2x2 + 30 + x + -2x2

Combine like terms: -90 + 30 = -60
-60 + -4x + x + 5x2 + -2x2 = -30 + -1x + 2x2 + 30 + x + -2x2

Combine like terms: -4x + x = -3x
-60 + -3x + 5x2 + -2x2 = -30 + -1x + 2x2 + 30 + x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-60 + -3x + 3x2 = -30 + -1x + 2x2 + 30 + x + -2x2

Reorder the terms:
-60 + -3x + 3x2 = -30 + 30 + -1x + x + 2x2 + -2x2

Combine like terms: -30 + 30 = 0
-60 + -3x + 3x2 = 0 + -1x + x + 2x2 + -2x2
-60 + -3x + 3x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
-60 + -3x + 3x2 = 0 + 2x2 + -2x2
-60 + -3x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-60 + -3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + -1x + x2) = 0

Factor a trinomial.
3((-4 + -1x)(5 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-4, 5}

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