x^2=9(10-x)

Solution for x^2=9(10-x) equation:

Simplifying
x2 = 9(10 + -1x)
x2 = (10 * 9 + -1x * 9)
x2 = (90 + -9x)

Solving
x2 = 90 + -9x

Solving for variable 'x'.

Reorder the terms:
-90 + 9x + x2 = 90 + -9x + -90 + 9x

Reorder the terms:
-90 + 9x + x2 = 90 + -90 + -9x + 9x

Combine like terms: 90 + -90 = 0
-90 + 9x + x2 = 0 + -9x + 9x
-90 + 9x + x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-90 + 9x + x2 = 0

Factor a trinomial.
(-15 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
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 = {-15, 6}