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((-10 + -1x)(5 + -1x)) = 0

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