12x-2x^2=x+5

Solution for 12x-2x^2=x+5 equation:

Simplifying
12x + -2x2 = x + 5

Reorder the terms:
12x + -2x2 = 5 + x

Solving
12x + -2x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
-5 + 12x + -1x + -2x2 = 5 + x + -5 + -1x

Combine like terms: 12x + -1x = 11x
-5 + 11x + -2x2 = 5 + x + -5 + -1x

Reorder the terms:
-5 + 11x + -2x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-5 + 11x + -2x2 = 0 + x + -1x
-5 + 11x + -2x2 = x + -1x

Combine like terms: x + -1x = 0
-5 + 11x + -2x2 = 0

Factor a trinomial.
(-5 + x)(1 + -2x) = 0

Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {5, 0.5}