x^2=15x+100

Solution for x^2=15x+100 equation:

Simplifying
x2 = 15x + 100

Reorder the terms:
x2 = 100 + 15x

Solving
x2 = 100 + 15x

Solving for variable 'x'.

Reorder the terms:
-100 + -15x + x2 = 100 + 15x + -100 + -15x

Reorder the terms:
-100 + -15x + x2 = 100 + -100 + 15x + -15x

Combine like terms: 100 + -100 = 0
-100 + -15x + x2 = 0 + 15x + -15x
-100 + -15x + x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-100 + -15x + x2 = 0

Factor a trinomial.
(-5 + -1x)(20 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {-5, 20}