10x+12=x^2+x-10

Solution for 10x+12=x^2+x-10 equation:

Simplifying
10x + 12 = x2 + x + -10

Reorder the terms:
12 + 10x = x2 + x + -10

Reorder the terms:
12 + 10x = -10 + x + x2

Solving
12 + 10x = -10 + x + x2

Solving for variable 'x'.

Reorder the terms:
12 + 10 + 10x + -1x + -1x2 = -10 + x + x2 + 10 + -1x + -1x2

Combine like terms: 12 + 10 = 22
22 + 10x + -1x + -1x2 = -10 + x + x2 + 10 + -1x + -1x2

Combine like terms: 10x + -1x = 9x
22 + 9x + -1x2 = -10 + x + x2 + 10 + -1x + -1x2

Reorder the terms:
22 + 9x + -1x2 = -10 + 10 + x + -1x + x2 + -1x2

Combine like terms: -10 + 10 = 0
22 + 9x + -1x2 = 0 + x + -1x + x2 + -1x2
22 + 9x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
22 + 9x + -1x2 = 0 + x2 + -1x2
22 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
22 + 9x + -1x2 = 0

Factor a trinomial.
(11 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {11, -2}