(x-5)(x+10)=100

Solution for (x-5)(x+10)=100 equation:

Simplifying
(x + -5)(x + 10) = 100

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

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

Multiply (-5 + x) * (10 + x)
(-5(10 + x) + x(10 + x)) = 100
((10 * -5 + x * -5) + x(10 + x)) = 100
((-50 + -5x) + x(10 + x)) = 100
(-50 + -5x + (10 * x + x * x)) = 100
(-50 + -5x + (10x + x2)) = 100

Combine like terms: -5x + 10x = 5x
(-50 + 5x + x2) = 100

Solving
-50 + 5x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
-50 + -100 + 5x + x2 = 100 + -100

Combine like terms: -50 + -100 = -150
-150 + 5x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-150 + 5x + x2 = 0

Factor a trinomial.
(-15 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
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 = {-15, 10}