(10+x)(10+(x+5))=300

Solution for (10+x)(10+(x+5))=300 equation:

Simplifying
(10 + x)(10 + (x + 5)) = 300

Reorder the terms:
(10 + x)(10 + (5 + x)) = 300

Remove parenthesis around (5 + x)
(10 + x)(10 + 5 + x) = 300

Combine like terms: 10 + 5 = 15
(10 + x)(15 + x) = 300

Multiply (10 + x) * (15 + x)
(10(15 + x) + x(15 + x)) = 300
((15 * 10 + x * 10) + x(15 + x)) = 300
((150 + 10x) + x(15 + x)) = 300
(150 + 10x + (15 * x + x * x)) = 300
(150 + 10x + (15x + x2)) = 300

Combine like terms: 10x + 15x = 25x
(150 + 25x + x2) = 300

Solving
150 + 25x + x2 = 300

Solving for variable 'x'.

Reorder the terms:
150 + -300 + 25x + x2 = 300 + -300

Combine like terms: 150 + -300 = -150
-150 + 25x + x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-150 + 25x + x2 = 0

Factor a trinomial.
(-30 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-30 + -1x)' equal to zero and attempt to solve:

Simplifying
-30 + -1x = 0

Solving
-30 + -1x = 0

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

Add '30' to each side of the equation.
-30 + 30 + -1x = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -1x = 0 + 30
-1x = 0 + 30

Combine like terms: 0 + 30 = 30
-1x = 30

Divide each side by '-1'.
x = -30

Simplifying
x = -30
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 = {-30, 5}