32=x+2+x+6+x^2-2x+3x-4

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Solution for 32=x+2+x+6+x^2-2x+3x-4 equation: 


Simplifying
32 = x + 2 + x + 6 + x2 + -2x + 3x + -4

Reorder the terms:
32 = 2 + 6 + -4 + x + x + -2x + 3x + x2

Combine like terms: 2 + 6 = 8
32 = 8 + -4 + x + x + -2x + 3x + x2

Combine like terms: 8 + -4 = 4
32 = 4 + x + x + -2x + 3x + x2

Combine like terms: x + x = 2x
32 = 4 + 2x + -2x + 3x + x2

Combine like terms: 2x + -2x = 0
32 = 4 + 0 + 3x + x2
32 = 4 + 3x + x2

Solving
32 = 4 + 3x + x2

Solving for variable 'x'.

Combine like terms: 32 + -4 = 28
28 + -3x + -1x2 = 4 + 3x + x2 + -4 + -3x + -1x2

Reorder the terms:
28 + -3x + -1x2 = 4 + -4 + 3x + -3x + x2 + -1x2

Combine like terms: 4 + -4 = 0
28 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2
28 + -3x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
28 + -3x + -1x2 = 0 + x2 + -1x2
28 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
28 + -3x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(7 + 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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

Simplifying
x = -7
Solution
x = {4, -7}

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