12x-84=x^2-13x+30

Solution for 12x-84=x^2-13x+30 equation:

Simplifying
12x + -84 = x2 + -13x + 30

Reorder the terms:
-84 + 12x = x2 + -13x + 30

Reorder the terms:
-84 + 12x = 30 + -13x + x2

Solving
-84 + 12x = 30 + -13x + x2

Solving for variable 'x'.

Reorder the terms:
-84 + -30 + 12x + 13x + -1x2 = 30 + -13x + x2 + -30 + 13x + -1x2

Combine like terms: -84 + -30 = -114
-114 + 12x + 13x + -1x2 = 30 + -13x + x2 + -30 + 13x + -1x2

Combine like terms: 12x + 13x = 25x
-114 + 25x + -1x2 = 30 + -13x + x2 + -30 + 13x + -1x2

Reorder the terms:
-114 + 25x + -1x2 = 30 + -30 + -13x + 13x + x2 + -1x2

Combine like terms: 30 + -30 = 0
-114 + 25x + -1x2 = 0 + -13x + 13x + x2 + -1x2
-114 + 25x + -1x2 = -13x + 13x + x2 + -1x2

Combine like terms: -13x + 13x = 0
-114 + 25x + -1x2 = 0 + x2 + -1x2
-114 + 25x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-114 + 25x + -1x2 = 0

Factor a trinomial.
(-19 + x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-19 + x)' equal to zero and attempt to solve:

Simplifying
-19 + x = 0

Solving
-19 + x = 0

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

Add '19' to each side of the equation.
-19 + 19 + x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + x = 0 + 19
x = 0 + 19

Combine like terms: 0 + 19 = 19
x = 19

Simplifying
x = 19
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 = {19, 6}