x+3+x+7+x^2-2x+3x-2=48

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Solution for x+3+x+7+x^2-2x+3x-2=48 equation: 


Simplifying
x + 3 + x + 7 + x2 + -2x + 3x + -2 = 48

Reorder the terms:
3 + 7 + -2 + x + x + -2x + 3x + x2 = 48

Combine like terms: 3 + 7 = 10
10 + -2 + x + x + -2x + 3x + x2 = 48

Combine like terms: 10 + -2 = 8
8 + x + x + -2x + 3x + x2 = 48

Combine like terms: x + x = 2x
8 + 2x + -2x + 3x + x2 = 48

Combine like terms: 2x + -2x = 0
8 + 0 + 3x + x2 = 48
8 + 3x + x2 = 48

Solving
8 + 3x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
8 + -48 + 3x + x2 = 48 + -48

Combine like terms: 8 + -48 = -40
-40 + 3x + x2 = 48 + -48

Combine like terms: 48 + -48 = 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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