2x+12=10x-x^2

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

Simplifying
2x + 12 = 10x + -1x2

Reorder the terms:
12 + 2x = 10x + -1x2

Solving
12 + 2x = 10x + -1x2

Solving for variable 'x'.

Combine like terms: 2x + -10x = -8x
12 + -8x + x2 = 10x + -1x2 + -10x + x2

Reorder the terms:
12 + -8x + x2 = 10x + -10x + -1x2 + x2

Combine like terms: 10x + -10x = 0
12 + -8x + x2 = 0 + -1x2 + x2
12 + -8x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
12 + -8x + x2 = 0

Factor a trinomial.
(2 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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 = {2, 6}