x(1-x)=25(x-1)

Solution for x(1-x)=25(x-1) equation:

Simplifying
x(1 + -1x) = 25(x + -1)
(1 * x + -1x * x) = 25(x + -1)
(1x + -1x2) = 25(x + -1)

Reorder the terms:
1x + -1x2 = 25(-1 + x)
1x + -1x2 = (-1 * 25 + x * 25)
1x + -1x2 = (-25 + 25x)

Solving
1x + -1x2 = -25 + 25x

Solving for variable 'x'.

Reorder the terms:
25 + 1x + -25x + -1x2 = -25 + 25x + 25 + -25x

Combine like terms: 1x + -25x = -24x
25 + -24x + -1x2 = -25 + 25x + 25 + -25x

Reorder the terms:
25 + -24x + -1x2 = -25 + 25 + 25x + -25x

Combine like terms: -25 + 25 = 0
25 + -24x + -1x2 = 0 + 25x + -25x
25 + -24x + -1x2 = 25x + -25x

Combine like terms: 25x + -25x = 0
25 + -24x + -1x2 = 0

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(25 + x)' equal to zero and attempt to solve:

Simplifying
25 + x = 0

Solving
25 + x = 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 + x = 0 + -25

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

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

Simplifying
x = -25
Solution
x = {1, -25}