x+3+x+5+3x-4+x^2-3x=52

Solution for x+3+x+5+3x-4+x^2-3x=52 equation:

Simplifying
x + 3 + x + 5 + 3x + -4 + x2 + -3x = 52

Reorder the terms:
3 + 5 + -4 + x + x + 3x + -3x + x2 = 52

Combine like terms: 3 + 5 = 8
8 + -4 + x + x + 3x + -3x + x2 = 52

Combine like terms: 8 + -4 = 4
4 + x + x + 3x + -3x + x2 = 52

Combine like terms: x + x = 2x
4 + 2x + 3x + -3x + x2 = 52

Combine like terms: 2x + 3x = 5x
4 + 5x + -3x + x2 = 52

Combine like terms: 5x + -3x = 2x
4 + 2x + x2 = 52

Solving
4 + 2x + x2 = 52

Solving for variable 'x'.

Reorder the terms:
4 + -52 + 2x + x2 = 52 + -52

Combine like terms: 4 + -52 = -48
-48 + 2x + x2 = 52 + -52

Combine like terms: 52 + -52 = 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}