x+4+x+7+3x-3+x^2-3x=43

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Solution for x+4+x+7+3x-3+x^2-3x=43 equation: 


Simplifying
x + 4 + x + 7 + 3x + -3 + x2 + -3x = 43

Reorder the terms:
4 + 7 + -3 + x + x + 3x + -3x + x2 = 43

Combine like terms: 4 + 7 = 11
11 + -3 + x + x + 3x + -3x + x2 = 43

Combine like terms: 11 + -3 = 8
8 + x + x + 3x + -3x + x2 = 43

Combine like terms: x + x = 2x
8 + 2x + 3x + -3x + x2 = 43

Combine like terms: 2x + 3x = 5x
8 + 5x + -3x + x2 = 43

Combine like terms: 5x + -3x = 2x
8 + 2x + x2 = 43

Solving
8 + 2x + x2 = 43

Solving for variable 'x'.

Reorder the terms:
8 + -43 + 2x + x2 = 43 + -43

Combine like terms: 8 + -43 = -35
-35 + 2x + x2 = 43 + -43

Combine like terms: 43 + -43 = 0
-35 + 2x + x2 = 0

Factor a trinomial.
(-7 + -1x)(5 + -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 '(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 = {-7, 5}

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