(x+5)+(x+3)+(3x-8)+(x^2-3x)=120

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Solution for (x+5)+(x+3)+(3x-8)+(x^2-3x)=120 equation: 


Simplifying
(x + 5) + (x + 3) + (3x + -8) + (x2 + -3x) = 120

Reorder the terms:
(5 + x) + (x + 3) + (3x + -8) + (x2 + -3x) = 120

Remove parenthesis around (5 + x)
5 + x + (x + 3) + (3x + -8) + (x2 + -3x) = 120

Reorder the terms:
5 + x + (3 + x) + (3x + -8) + (x2 + -3x) = 120

Remove parenthesis around (3 + x)
5 + x + 3 + x + (3x + -8) + (x2 + -3x) = 120

Reorder the terms:
5 + x + 3 + x + (-8 + 3x) + (x2 + -3x) = 120

Remove parenthesis around (-8 + 3x)
5 + x + 3 + x + -8 + 3x + (x2 + -3x) = 120

Reorder the terms:
5 + x + 3 + x + -8 + 3x + (-3x + x2) = 120

Remove parenthesis around (-3x + x2)
5 + x + 3 + x + -8 + 3x + -3x + x2 = 120

Reorder the terms:
5 + 3 + -8 + x + x + 3x + -3x + x2 = 120

Combine like terms: 5 + 3 = 8
8 + -8 + x + x + 3x + -3x + x2 = 120

Combine like terms: 8 + -8 = 0
0 + x + x + 3x + -3x + x2 = 120
x + x + 3x + -3x + x2 = 120

Combine like terms: x + x = 2x
2x + 3x + -3x + x2 = 120

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

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

Solving
2x + x2 = 120

Solving for variable 'x'.

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

Combine like terms: 120 + -120 = 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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