x(x-10)=75

Solution for x(x-10)=75 equation:

Simplifying
x(x + -10) = 75

Reorder the terms:
x(-10 + x) = 75
(-10 * x + x * x) = 75
(-10x + x2) = 75

Solving
-10x + x2 = 75

Solving for variable 'x'.

Reorder the terms:
-75 + -10x + x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-75 + -10x + x2 = 0

Factor a trinomial.
(-5 + -1x)(15 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
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 = {-5, 15}