30x=-2x^2-100

Solution for 30x=-2x^2-100 equation:

Simplifying
30x = -2x2 + -100

Reorder the terms:
30x = -100 + -2x2

Solving
30x = -100 + -2x2

Solving for variable 'x'.

Reorder the terms:
100 + 30x + 2x2 = -100 + -2x2 + 100 + 2x2

Reorder the terms:
100 + 30x + 2x2 = -100 + 100 + -2x2 + 2x2

Combine like terms: -100 + 100 = 0
100 + 30x + 2x2 = 0 + -2x2 + 2x2
100 + 30x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
100 + 30x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(50 + 15x + x2) = 0

Factor a trinomial.
2((10 + x)(5 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 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 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-10, -5}