x^2(x-2)25(x-2)=0

Solution for x^2(x-2)25(x-2)=0 equation:

Simplifying
x2(x + -2) * 25(x + -2) = 0

Reorder the terms:
x2(-2 + x) * 25(x + -2) = 0

Reorder the terms:
x2(-2 + x) * 25(-2 + x) = 0

Reorder the terms for easier multiplication:
25x2(-2 + x)(-2 + x) = 0

Multiply (-2 + x) * (-2 + x)
25x2(-2(-2 + x) + x(-2 + x)) = 0
25x2((-2 * -2 + x * -2) + x(-2 + x)) = 0
25x2((4 + -2x) + x(-2 + x)) = 0
25x2(4 + -2x + (-2 * x + x * x)) = 0
25x2(4 + -2x + (-2x + x2)) = 0

Combine like terms: -2x + -2x = -4x
25x2(4 + -4x + x2) = 0
(4 * 25x2 + -4x * 25x2 + x2 * 25x2) = 0
(100x2 + -100x3 + 25x4) = 0

Solving
100x2 + -100x3 + 25x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '25x2'.
25x2(4 + -4x + x2) = 0

Factor a trinomial.
25x2((2 + -1x)(2 + -1x)) = 0

Ignore the factor 25.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 2, 2}