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

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

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

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

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

Multiply (-5 + a) * (10 + a)
(-5(10 + a) + a(10 + a)) = 100
((10 * -5 + a * -5) + a(10 + a)) = 100
((-50 + -5a) + a(10 + a)) = 100
(-50 + -5a + (10 * a + a * a)) = 100
(-50 + -5a + (10a + a2)) = 100

Combine like terms: -5a + 10a = 5a
(-50 + 5a + a2) = 100

Solving
-50 + 5a + a2 = 100

Solving for variable 'a'.

Reorder the terms:
-50 + -100 + 5a + a2 = 100 + -100

Combine like terms: -50 + -100 = -150
-150 + 5a + a2 = 100 + -100

Combine like terms: 100 + -100 = 0
-150 + 5a + a2 = 0

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

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

Simplifying
-15 + -1a = 0

Solving
-15 + -1a = 0

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

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

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

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

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

Simplifying
a = -15
Subproblem 2
Set the factor '(10 + -1a)' equal to zero and attempt to solve:

Simplifying
10 + -1a = 0

Solving
10 + -1a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1a = 0 + -10
-1a = 0 + -10

Combine like terms: 0 + -10 = -10
-1a = -10

Divide each side by '-1'.
a = 10

Simplifying
a = 10
Solution
a = {-15, 10}