x^2+x-45=9x+3

Solution for x^2+x-45=9x+3 equation:

Simplifying
x2 + x + -45 = 9x + 3

Reorder the terms:
-45 + x + x2 = 9x + 3

Reorder the terms:
-45 + x + x2 = 3 + 9x

Solving
-45 + x + x2 = 3 + 9x

Solving for variable 'x'.

Reorder the terms:
-45 + -3 + x + -9x + x2 = 3 + 9x + -3 + -9x

Combine like terms: -45 + -3 = -48
-48 + x + -9x + x2 = 3 + 9x + -3 + -9x

Combine like terms: x + -9x = -8x
-48 + -8x + x2 = 3 + 9x + -3 + -9x

Reorder the terms:
-48 + -8x + x2 = 3 + -3 + 9x + -9x

Combine like terms: 3 + -3 = 0
-48 + -8x + x2 = 0 + 9x + -9x
-48 + -8x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-48 + -8x + x2 = 0

Factor a trinomial.
(-4 + -1x)(12 + -1x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

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

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

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-4, 12}