(X+10)*(X+15)-150=150

Solution for (X+10)*(X+15)-150=150 equation:

Simplifying
(X + 10)(X + 15) + -150 = 150

Reorder the terms:
(10 + X)(X + 15) + -150 = 150

Reorder the terms:
(10 + X)(15 + X) + -150 = 150

Multiply (10 + X) * (15 + X)
(10(15 + X) + X(15 + X)) + -150 = 150
((15 * 10 + X * 10) + X(15 + X)) + -150 = 150
((150 + 10X) + X(15 + X)) + -150 = 150
(150 + 10X + (15 * X + X * X)) + -150 = 150
(150 + 10X + (15X + X2)) + -150 = 150

Combine like terms: 10X + 15X = 25X
(150 + 25X + X2) + -150 = 150

Reorder the terms:
150 + -150 + 25X + X2 = 150

Combine like terms: 150 + -150 = 0
0 + 25X + X2 = 150
25X + X2 = 150

Solving
25X + X2 = 150

Solving for variable 'X'.

Reorder the terms:
-150 + 25X + X2 = 150 + -150

Combine like terms: 150 + -150 = 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}