35=(x+5)+(x+8)+(x^2-2x)+(2x-2)

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Solution for 35=(x+5)+(x+8)+(x^2-2x)+(2x-2) equation: 


Simplifying
35 = (x + 5) + (x + 8) + (x2 + -2x) + (2x + -2)

Reorder the terms:
35 = (5 + x) + (x + 8) + (x2 + -2x) + (2x + -2)

Remove parenthesis around (5 + x)
35 = 5 + x + (x + 8) + (x2 + -2x) + (2x + -2)

Reorder the terms:
35 = 5 + x + (8 + x) + (x2 + -2x) + (2x + -2)

Remove parenthesis around (8 + x)
35 = 5 + x + 8 + x + (x2 + -2x) + (2x + -2)

Reorder the terms:
35 = 5 + x + 8 + x + (-2x + x2) + (2x + -2)

Remove parenthesis around (-2x + x2)
35 = 5 + x + 8 + x + -2x + x2 + (2x + -2)

Reorder the terms:
35 = 5 + x + 8 + x + -2x + x2 + (-2 + 2x)

Remove parenthesis around (-2 + 2x)
35 = 5 + x + 8 + x + -2x + x2 + -2 + 2x

Reorder the terms:
35 = 5 + 8 + -2 + x + x + -2x + 2x + x2

Combine like terms: 5 + 8 = 13
35 = 13 + -2 + x + x + -2x + 2x + x2

Combine like terms: 13 + -2 = 11
35 = 11 + x + x + -2x + 2x + x2

Combine like terms: x + x = 2x
35 = 11 + 2x + -2x + 2x + x2

Combine like terms: 2x + -2x = 0
35 = 11 + 0 + 2x + x2
35 = 11 + 2x + x2

Solving
35 = 11 + 2x + x2

Solving for variable 'x'.

Combine like terms: 35 + -11 = 24
24 + -2x + -1x2 = 11 + 2x + x2 + -11 + -2x + -1x2

Reorder the terms:
24 + -2x + -1x2 = 11 + -11 + 2x + -2x + x2 + -1x2

Combine like terms: 11 + -11 = 0
24 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2
24 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
24 + -2x + -1x2 = 0 + x2 + -1x2
24 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + -2x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(6 + x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {4, -6}

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