(x-10)*(x+25)=0

Solution for (x-10)*(x+25)=0 equation:

Simplifying
(x + -10)(x + 25) = 0

Reorder the terms:
(-10 + x)(x + 25) = 0

Reorder the terms:
(-10 + x)(25 + x) = 0

Multiply (-10 + x) * (25 + x)
(-10(25 + x) + x(25 + x)) = 0
((25 * -10 + x * -10) + x(25 + x)) = 0
((-250 + -10x) + x(25 + x)) = 0
(-250 + -10x + (25 * x + x * x)) = 0
(-250 + -10x + (25x + x2)) = 0

Combine like terms: -10x + 25x = 15x
(-250 + 15x + x2) = 0

Solving
-250 + 15x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-25 + -1x)(10 + -1x) = 0

Subproblem 1
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
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 = {-25, 10}