6x^2-8x-90=5x^2-9x

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Solution for 6x^2-8x-90=5x^2-9x equation: 


Simplifying
6x2 + -8x + -90 = 5x2 + -9x

Reorder the terms:
-90 + -8x + 6x2 = 5x2 + -9x

Reorder the terms:
-90 + -8x + 6x2 = -9x + 5x2

Solving
-90 + -8x + 6x2 = -9x + 5x2

Solving for variable 'x'.

Reorder the terms:
-90 + -8x + 9x + 6x2 + -5x2 = -9x + 5x2 + 9x + -5x2

Combine like terms: -8x + 9x = 1x
-90 + 1x + 6x2 + -5x2 = -9x + 5x2 + 9x + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
-90 + 1x + 1x2 = -9x + 5x2 + 9x + -5x2

Reorder the terms:
-90 + 1x + 1x2 = -9x + 9x + 5x2 + -5x2

Combine like terms: -9x + 9x = 0
-90 + 1x + 1x2 = 0 + 5x2 + -5x2
-90 + 1x + 1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-90 + 1x + 1x2 = 0

Factor a trinomial.
(-10 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-10, 9}

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