(x-10)(x-15)=0

Solution for (x-10)(x-15)=0 equation:

Simplifying
(x + -10)(x + -15) = 0

Reorder the terms:
(-10 + x)(x + -15) = 0

Reorder the terms:
(-10 + x)(-15 + x) = 0

Multiply (-10 + x) * (-15 + x)
(-10(-15 + x) + x(-15 + x)) = 0
((-15 * -10 + x * -10) + x(-15 + x)) = 0
((150 + -10x) + x(-15 + x)) = 0
(150 + -10x + (-15 * x + x * x)) = 0
(150 + -10x + (-15x + x2)) = 0

Combine like terms: -10x + -15x = -25x
(150 + -25x + x2) = 0

Solving
150 + -25x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(10 + -1x)(15 + -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 '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {10, 15}