x+5+x+6+x^2-3x+3x-4=42

Solution for x+5+x+6+x^2-3x+3x-4=42 equation:

Simplifying
x + 5 + x + 6 + x2 + -3x + 3x + -4 = 42

Reorder the terms:
5 + 6 + -4 + x + x + -3x + 3x + x2 = 42

Combine like terms: 5 + 6 = 11
11 + -4 + x + x + -3x + 3x + x2 = 42

Combine like terms: 11 + -4 = 7
7 + x + x + -3x + 3x + x2 = 42

Combine like terms: x + x = 2x
7 + 2x + -3x + 3x + x2 = 42

Combine like terms: 2x + -3x = -1x
7 + -1x + 3x + x2 = 42

Combine like terms: -1x + 3x = 2x
7 + 2x + x2 = 42

Solving
7 + 2x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
7 + -42 + 2x + x2 = 42 + -42

Combine like terms: 7 + -42 = -35
-35 + 2x + x2 = 42 + -42

Combine like terms: 42 + -42 = 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}