9x^2-97x+312=6x^2-58x+186

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Solution for 9x^2-97x+312=6x^2-58x+186 equation: 


Simplifying
9x2 + -97x + 312 = 6x2 + -58x + 186

Reorder the terms:
312 + -97x + 9x2 = 6x2 + -58x + 186

Reorder the terms:
312 + -97x + 9x2 = 186 + -58x + 6x2

Solving
312 + -97x + 9x2 = 186 + -58x + 6x2

Solving for variable 'x'.

Reorder the terms:
312 + -186 + -97x + 58x + 9x2 + -6x2 = 186 + -58x + 6x2 + -186 + 58x + -6x2

Combine like terms: 312 + -186 = 126
126 + -97x + 58x + 9x2 + -6x2 = 186 + -58x + 6x2 + -186 + 58x + -6x2

Combine like terms: -97x + 58x = -39x
126 + -39x + 9x2 + -6x2 = 186 + -58x + 6x2 + -186 + 58x + -6x2

Combine like terms: 9x2 + -6x2 = 3x2
126 + -39x + 3x2 = 186 + -58x + 6x2 + -186 + 58x + -6x2

Reorder the terms:
126 + -39x + 3x2 = 186 + -186 + -58x + 58x + 6x2 + -6x2

Combine like terms: 186 + -186 = 0
126 + -39x + 3x2 = 0 + -58x + 58x + 6x2 + -6x2
126 + -39x + 3x2 = -58x + 58x + 6x2 + -6x2

Combine like terms: -58x + 58x = 0
126 + -39x + 3x2 = 0 + 6x2 + -6x2
126 + -39x + 3x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
126 + -39x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(42 + -13x + x2) = 0

Factor a trinomial.
3((6 + -1x)(7 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {6, 7}

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