x^2+x-19=29-x

Solution for x^2+x-19=29-x equation:

Simplifying
x2 + x + -19 = 29 + -1x

Reorder the terms:
-19 + x + x2 = 29 + -1x

Solving
-19 + x + x2 = 29 + -1x

Solving for variable 'x'.

Reorder the terms:
-19 + -29 + x + x + x2 = 29 + -1x + -29 + x

Combine like terms: -19 + -29 = -48
-48 + x + x + x2 = 29 + -1x + -29 + x

Combine like terms: x + x = 2x
-48 + 2x + x2 = 29 + -1x + -29 + x

Reorder the terms:
-48 + 2x + x2 = 29 + -29 + -1x + x

Combine like terms: 29 + -29 = 0
-48 + 2x + x2 = 0 + -1x + x
-48 + 2x + x2 = -1x + x

Combine like terms: -1x + x = 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}