90x+2160=x^2+48x

Solution for 90x+2160=x^2+48x equation:

Simplifying
90x + 2160 = x2 + 48x

Reorder the terms:
2160 + 90x = x2 + 48x

Reorder the terms:
2160 + 90x = 48x + x2

Solving
2160 + 90x = 48x + x2

Solving for variable 'x'.

Combine like terms: 90x + -48x = 42x
2160 + 42x + -1x2 = 48x + x2 + -48x + -1x2

Reorder the terms:
2160 + 42x + -1x2 = 48x + -48x + x2 + -1x2

Combine like terms: 48x + -48x = 0
2160 + 42x + -1x2 = 0 + x2 + -1x2
2160 + 42x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2160 + 42x + -1x2 = 0

Factor a trinomial.
(72 + -1x)(30 + x) = 0

Subproblem 1
Set the factor '(72 + -1x)' equal to zero and attempt to solve:

Simplifying
72 + -1x = 0

Solving
72 + -1x = 0

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

Add '-72' to each side of the equation.
72 + -72 + -1x = 0 + -72

Combine like terms: 72 + -72 = 0
0 + -1x = 0 + -72
-1x = 0 + -72

Combine like terms: 0 + -72 = -72
-1x = -72

Divide each side by '-1'.
x = 72

Simplifying
x = 72
Subproblem 2
Set the factor '(30 + x)' equal to zero and attempt to solve:

Simplifying
30 + x = 0

Solving
30 + x = 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 + x = 0 + -30

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

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

Simplifying
x = -30
Solution
x = {72, -30}