2x(x-5)=100

Solution for 2x(x-5)=100 equation:

Simplifying
2x(x + -5) = 100

Reorder the terms:
2x(-5 + x) = 100
(-5 * 2x + x * 2x) = 100
(-10x + 2x2) = 100

Solving
-10x + 2x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + -10x + 2x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + -5x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(10 + -1x)) = 0

Ignore the factor 2.
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 '(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 = {-5, 10}