x(x-1)=15x+80

Solution for x(x-1)=15x+80 equation:

Simplifying
x(x + -1) = 15x + 80

Reorder the terms:
x(-1 + x) = 15x + 80
(-1 * x + x * x) = 15x + 80
(-1x + x2) = 15x + 80

Reorder the terms:
-1x + x2 = 80 + 15x

Solving
-1x + x2 = 80 + 15x

Solving for variable 'x'.

Reorder the terms:
-80 + -1x + -15x + x2 = 80 + 15x + -80 + -15x

Combine like terms: -1x + -15x = -16x
-80 + -16x + x2 = 80 + 15x + -80 + -15x

Reorder the terms:
-80 + -16x + x2 = 80 + -80 + 15x + -15x

Combine like terms: 80 + -80 = 0
-80 + -16x + x2 = 0 + 15x + -15x
-80 + -16x + x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-80 + -16x + x2 = 0

Factor a trinomial.
(-4 + -1x)(20 + -1x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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 = {-4, 20}