x^2+6x=4x+120

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Solution for x^2+6x=4x+120 equation: 


Simplifying
x2 + 6x = 4x + 120

Reorder the terms:
6x + x2 = 4x + 120

Reorder the terms:
6x + x2 = 120 + 4x

Solving
6x + x2 = 120 + 4x

Solving for variable 'x'.

Reorder the terms:
-120 + 6x + -4x + x2 = 120 + 4x + -120 + -4x

Combine like terms: 6x + -4x = 2x
-120 + 2x + x2 = 120 + 4x + -120 + -4x

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

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

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

Factor a trinomial.
(-12 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

Subproblem 2
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
Solution
x = {-12, 10}

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