a^2+90a-1000=0

Solution for a^2+90a-1000=0 equation:

Simplifying
a2 + 90a + -1000 = 0

Reorder the terms:
-1000 + 90a + a2 = 0

Solving
-1000 + 90a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-100 + -1a)(10 + -1a) = 0

Subproblem 1
Set the factor '(-100 + -1a)' equal to zero and attempt to solve:

Simplifying
-100 + -1a = 0

Solving
-100 + -1a = 0

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

Add '100' to each side of the equation.
-100 + 100 + -1a = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -1a = 0 + 100
-1a = 0 + 100

Combine like terms: 0 + 100 = 100
-1a = 100

Divide each side by '-1'.
a = -100

Simplifying
a = -100
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 = {-100, 10}