(x+10)(2x+30)=100

Solution for (x+10)(2x+30)=100 equation:

Simplifying
(x + 10)(2x + 30) = 100

Reorder the terms:
(10 + x)(2x + 30) = 100

Reorder the terms:
(10 + x)(30 + 2x) = 100

Multiply (10 + x) * (30 + 2x)
(10(30 + 2x) + x(30 + 2x)) = 100
((30 * 10 + 2x * 10) + x(30 + 2x)) = 100
((300 + 20x) + x(30 + 2x)) = 100
(300 + 20x + (30 * x + 2x * x)) = 100
(300 + 20x + (30x + 2x2)) = 100

Combine like terms: 20x + 30x = 50x
(300 + 50x + 2x2) = 100

Solving
300 + 50x + 2x2 = 100

Solving for variable 'x'.

Reorder the terms:
300 + -100 + 50x + 2x2 = 100 + -100

Combine like terms: 300 + -100 = 200
200 + 50x + 2x2 = 100 + -100

Combine like terms: 100 + -100 = 0
200 + 50x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(100 + 25x + x2) = 0

Factor a trinomial.
2((20 + x)(5 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(20 + x)' equal to zero and attempt to solve:

Simplifying
20 + x = 0

Solving
20 + x = 0

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

Add '-20' to each side of the equation.
20 + -20 + x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + x = 0 + -20
x = 0 + -20

Combine like terms: 0 + -20 = -20
x = -20

Simplifying
x = -20
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {-20, -5}