0=-90-45x-5x^2

Solution for 0=-90-45x-5x^2 equation:

Simplifying
0 = -90 + -45x + -5x2

Solving
0 = -90 + -45x + -5x2

Solving for variable 'x'.

Combine like terms: 0 + 90 = 90
90 + 45x + 5x2 = -90 + -45x + -5x2 + 90 + 45x + 5x2

Reorder the terms:
90 + 45x + 5x2 = -90 + 90 + -45x + 45x + -5x2 + 5x2

Combine like terms: -90 + 90 = 0
90 + 45x + 5x2 = 0 + -45x + 45x + -5x2 + 5x2
90 + 45x + 5x2 = -45x + 45x + -5x2 + 5x2

Combine like terms: -45x + 45x = 0
90 + 45x + 5x2 = 0 + -5x2 + 5x2
90 + 45x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
90 + 45x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(18 + 9x + x2) = 0

Factor a trinomial.
5((6 + x)(3 + x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-6, -3}