x(x-21)=100

Solution for x(x-21)=100 equation:

Simplifying
x(x + -21) = 100

Reorder the terms:
x(-21 + x) = 100
(-21 * x + x * x) = 100
(-21x + x2) = 100

Solving
-21x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + -21x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + -21x + x2 = 0

Factor a trinomial.
(-4 + -1x)(25 + -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 '(25 + -1x)' equal to zero and attempt to solve:

Simplifying
25 + -1x = 0

Solving
25 + -1x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1x = 0 + -25
-1x = 0 + -25

Combine like terms: 0 + -25 = -25
-1x = -25

Divide each side by '-1'.
x = 25

Simplifying
x = 25
Solution
x = {-4, 25}