x^2+3x-3x-4+x+x+3+4=51

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Solution for x^2+3x-3x-4+x+x+3+4=51 equation: 


Simplifying
x2 + 3x + -3x + -4 + x + x + 3 + 4 = 51

Reorder the terms:
-4 + 3 + 4 + 3x + -3x + x + x + x2 = 51

Combine like terms: -4 + 3 = -1
-1 + 4 + 3x + -3x + x + x + x2 = 51

Combine like terms: -1 + 4 = 3
3 + 3x + -3x + x + x + x2 = 51

Combine like terms: 3x + -3x = 0
3 + 0 + x + x + x2 = 51
3 + x + x + x2 = 51

Combine like terms: x + x = 2x
3 + 2x + x2 = 51

Solving
3 + 2x + x2 = 51

Solving for variable 'x'.

Reorder the terms:
3 + -51 + 2x + x2 = 51 + -51

Combine like terms: 3 + -51 = -48
-48 + 2x + x2 = 51 + -51

Combine like terms: 51 + -51 = 0
-48 + 2x + x2 = 0

Factor a trinomial.
(-8 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-8, 6}

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