x^2+9=9x+45

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

Simplifying
x2 + 9 = 9x + 45

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

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

Solving
9 + x2 = 45 + 9x

Solving for variable 'x'.

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

Combine like terms: 9 + -45 = -36
-36 + -9x + x2 = 45 + 9x + -45 + -9x

Reorder the terms:
-36 + -9x + x2 = 45 + -45 + 9x + -9x

Combine like terms: 45 + -45 = 0
-36 + -9x + x2 = 0 + 9x + -9x
-36 + -9x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-36 + -9x + x2 = 0

Factor a trinomial.
(-3 + -1x)(12 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 12}