x^2+12x=37x+150

Solution for x^2+12x=37x+150 equation:

Simplifying
x2 + 12x = 37x + 150

Reorder the terms:
12x + x2 = 37x + 150

Reorder the terms:
12x + x2 = 150 + 37x

Solving
12x + x2 = 150 + 37x

Solving for variable 'x'.

Reorder the terms:
-150 + 12x + -37x + x2 = 150 + 37x + -150 + -37x

Combine like terms: 12x + -37x = -25x
-150 + -25x + x2 = 150 + 37x + -150 + -37x

Reorder the terms:
-150 + -25x + x2 = 150 + -150 + 37x + -37x

Combine like terms: 150 + -150 = 0
-150 + -25x + x2 = 0 + 37x + -37x
-150 + -25x + x2 = 37x + -37x

Combine like terms: 37x + -37x = 0
-150 + -25x + x2 = 0

Factor a trinomial.
(-5 + -1x)(30 + -1x) = 0

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Solution
x = {-5, 30}