(x-25)(x+50)=0

Solution for (x-25)(x+50)=0 equation:

Simplifying
(x + -25)(x + 50) = 0

Reorder the terms:
(-25 + x)(x + 50) = 0

Reorder the terms:
(-25 + x)(50 + x) = 0

Multiply (-25 + x) * (50 + x)
(-25(50 + x) + x(50 + x)) = 0
((50 * -25 + x * -25) + x(50 + x)) = 0
((-1250 + -25x) + x(50 + x)) = 0
(-1250 + -25x + (50 * x + x * x)) = 0
(-1250 + -25x + (50x + x2)) = 0

Combine like terms: -25x + 50x = 25x
(-1250 + 25x + x2) = 0

Solving
-1250 + 25x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-50 + -1x)(25 + -1x) = 0

Subproblem 1
Set the factor '(-50 + -1x)' equal to zero and attempt to solve:

Simplifying
-50 + -1x = 0

Solving
-50 + -1x = 0

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

Add '50' to each side of the equation.
-50 + 50 + -1x = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -1x = 0 + 50
-1x = 0 + 50

Combine like terms: 0 + 50 = 50
-1x = 50

Divide each side by '-1'.
x = -50

Simplifying
x = -50
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 = {-50, 25}