x+7+x+4+3x-2+x^2-2x=37

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Solution for x+7+x+4+3x-2+x^2-2x=37 equation: 


Simplifying
x + 7 + x + 4 + 3x + -2 + x2 + -2x = 37

Reorder the terms:
7 + 4 + -2 + x + x + 3x + -2x + x2 = 37

Combine like terms: 7 + 4 = 11
11 + -2 + x + x + 3x + -2x + x2 = 37

Combine like terms: 11 + -2 = 9
9 + x + x + 3x + -2x + x2 = 37

Combine like terms: x + x = 2x
9 + 2x + 3x + -2x + x2 = 37

Combine like terms: 2x + 3x = 5x
9 + 5x + -2x + x2 = 37

Combine like terms: 5x + -2x = 3x
9 + 3x + x2 = 37

Solving
9 + 3x + x2 = 37

Solving for variable 'x'.

Reorder the terms:
9 + -37 + 3x + x2 = 37 + -37

Combine like terms: 9 + -37 = -28
-28 + 3x + x2 = 37 + -37

Combine like terms: 37 + -37 = 0
-28 + 3x + x2 = 0

Factor a trinomial.
(-7 + -1x)(4 + -1x) = 0


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 '(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
Solution
x = {-7, 4}

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