x^2=20(x-5)

Solution for x^2=20(x-5) equation:

Simplifying
x2 = 20(x + -5)

Reorder the terms:
x2 = 20(-5 + x)
x2 = (-5 * 20 + x * 20)
x2 = (-100 + 20x)

Solving
x2 = -100 + 20x

Solving for variable 'x'.

Reorder the terms:
100 + -20x + x2 = -100 + 20x + 100 + -20x

Reorder the terms:
100 + -20x + x2 = -100 + 100 + 20x + -20x

Combine like terms: -100 + 100 = 0
100 + -20x + x2 = 0 + 20x + -20x
100 + -20x + x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
100 + -20x + x2 = 0

Factor a trinomial.
(10 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {10, 10}