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

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

Simplifying
x + 4 + x + 2 + 4x + -3 + x2 + -3x = 43

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

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

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

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

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

Combine like terms: 6x + -3x = 3x
3 + 3x + x2 = 43

Solving
3 + 3x + x2 = 43

Solving for variable 'x'.

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

Combine like terms: 3 + -43 = -40
-40 + 3x + x2 = 43 + -43

Combine like terms: 43 + -43 = 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}