x+3+x+2+x^2-2x+3x-4=41

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Solution for x+3+x+2+x^2-2x+3x-4=41 equation:


Simplifying
x + 3 + x + 2 + x2 + -2x + 3x + -4 = 41

Reorder the terms:
3 + 2 + -4 + x + x + -2x + 3x + x2 = 41

Combine like terms: 3 + 2 = 5
5 + -4 + x + x + -2x + 3x + x2 = 41

Combine like terms: 5 + -4 = 1
1 + x + x + -2x + 3x + x2 = 41

Combine like terms: x + x = 2x
1 + 2x + -2x + 3x + x2 = 41

Combine like terms: 2x + -2x = 0
1 + 0 + 3x + x2 = 41
1 + 3x + x2 = 41

Solving
1 + 3x + x2 = 41

Solving for variable 'x'.

Reorder the terms:
1 + -41 + 3x + x2 = 41 + -41

Combine like terms: 1 + -41 = -40
-40 + 3x + x2 = 41 + -41

Combine like terms: 41 + -41 = 0
-40 + 3x + x2 = 0

Factor a trinomial.
(-8 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-8, 5}

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