(10+x)*x=(90+x)

Solution for (10+x)*x=(90+x) equation:

Simplifying
(10 + x) * x = (90 + x)

Reorder the terms for easier multiplication:
x(10 + x) = (90 + x)
(10 * x + x * x) = (90 + x)
(10x + x2) = (90 + x)

Remove parenthesis around (90 + x)
10x + x2 = 90 + x

Solving
10x + x2 = 90 + x

Solving for variable 'x'.

Reorder the terms:
-90 + 10x + -1x + x2 = 90 + x + -90 + -1x

Combine like terms: 10x + -1x = 9x
-90 + 9x + x2 = 90 + x + -90 + -1x

Reorder the terms:
-90 + 9x + x2 = 90 + -90 + x + -1x

Combine like terms: 90 + -90 = 0
-90 + 9x + x2 = 0 + x + -1x
-90 + 9x + x2 = x + -1x

Combine like terms: x + -1x = 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}