5x(x-1)-6=x(3x-1)+120

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Solution for 5x(x-1)-6=x(3x-1)+120 equation: 


Simplifying
5x(x + -1) + -6 = x(3x + -1) + 120

Reorder the terms:
5x(-1 + x) + -6 = x(3x + -1) + 120
(-1 * 5x + x * 5x) + -6 = x(3x + -1) + 120
(-5x + 5x2) + -6 = x(3x + -1) + 120

Reorder the terms:
-6 + -5x + 5x2 = x(3x + -1) + 120

Reorder the terms:
-6 + -5x + 5x2 = x(-1 + 3x) + 120
-6 + -5x + 5x2 = (-1 * x + 3x * x) + 120
-6 + -5x + 5x2 = (-1x + 3x2) + 120

Reorder the terms:
-6 + -5x + 5x2 = 120 + -1x + 3x2

Solving
-6 + -5x + 5x2 = 120 + -1x + 3x2

Solving for variable 'x'.

Reorder the terms:
-6 + -120 + -5x + x + 5x2 + -3x2 = 120 + -1x + 3x2 + -120 + x + -3x2

Combine like terms: -6 + -120 = -126
-126 + -5x + x + 5x2 + -3x2 = 120 + -1x + 3x2 + -120 + x + -3x2

Combine like terms: -5x + x = -4x
-126 + -4x + 5x2 + -3x2 = 120 + -1x + 3x2 + -120 + x + -3x2

Combine like terms: 5x2 + -3x2 = 2x2
-126 + -4x + 2x2 = 120 + -1x + 3x2 + -120 + x + -3x2

Reorder the terms:
-126 + -4x + 2x2 = 120 + -120 + -1x + x + 3x2 + -3x2

Combine like terms: 120 + -120 = 0
-126 + -4x + 2x2 = 0 + -1x + x + 3x2 + -3x2
-126 + -4x + 2x2 = -1x + x + 3x2 + -3x2

Combine like terms: -1x + x = 0
-126 + -4x + 2x2 = 0 + 3x2 + -3x2
-126 + -4x + 2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-126 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-63 + -2x + x2) = 0

Factor a trinomial.
2((-7 + -1x)(9 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

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 = {-7, 9}

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