(x+4)+(x+6)+(x^2-3x)+(3x-2)-43=0

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Solution for (x+4)+(x+6)+(x^2-3x)+(3x-2)-43=0 equation: 


Simplifying
(x + 4) + (x + 6) + (x2 + -3x) + (3x + -2) + -43 = 0

Reorder the terms:
(4 + x) + (x + 6) + (x2 + -3x) + (3x + -2) + -43 = 0

Remove parenthesis around (4 + x)
4 + x + (x + 6) + (x2 + -3x) + (3x + -2) + -43 = 0

Reorder the terms:
4 + x + (6 + x) + (x2 + -3x) + (3x + -2) + -43 = 0

Remove parenthesis around (6 + x)
4 + x + 6 + x + (x2 + -3x) + (3x + -2) + -43 = 0

Reorder the terms:
4 + x + 6 + x + (-3x + x2) + (3x + -2) + -43 = 0

Remove parenthesis around (-3x + x2)
4 + x + 6 + x + -3x + x2 + (3x + -2) + -43 = 0

Reorder the terms:
4 + x + 6 + x + -3x + x2 + (-2 + 3x) + -43 = 0

Remove parenthesis around (-2 + 3x)
4 + x + 6 + x + -3x + x2 + -2 + 3x + -43 = 0

Reorder the terms:
4 + 6 + -2 + -43 + x + x + -3x + 3x + x2 = 0

Combine like terms: 4 + 6 = 10
10 + -2 + -43 + x + x + -3x + 3x + x2 = 0

Combine like terms: 10 + -2 = 8
8 + -43 + x + x + -3x + 3x + x2 = 0

Combine like terms: 8 + -43 = -35
-35 + x + x + -3x + 3x + x2 = 0

Combine like terms: x + x = 2x
-35 + 2x + -3x + 3x + x2 = 0

Combine like terms: 2x + -3x = -1x
-35 + -1x + 3x + x2 = 0

Combine like terms: -1x + 3x = 2x
-35 + 2x + x2 = 0

Solving
-35 + 2x + x2 = 0

Solving for variable 'x'.

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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