12x-1=x^2+35

Solution for 12x-1=x^2+35 equation:

Simplifying
12x + -1 = x2 + 35

Reorder the terms:
-1 + 12x = x2 + 35

Reorder the terms:
-1 + 12x = 35 + x2

Solving
-1 + 12x = 35 + x2

Solving for variable 'x'.

Reorder the terms:
-1 + -35 + 12x + -1x2 = 35 + x2 + -35 + -1x2

Combine like terms: -1 + -35 = -36
-36 + 12x + -1x2 = 35 + x2 + -35 + -1x2

Reorder the terms:
-36 + 12x + -1x2 = 35 + -35 + x2 + -1x2

Combine like terms: 35 + -35 = 0
-36 + 12x + -1x2 = 0 + x2 + -1x2
-36 + 12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + 12x + -1x2 = 0

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

Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
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 = {6, 6}