4x^2+100x=-600

Solution for 4x^2+100x=-600 equation:

Simplifying
4x2 + 100x = -600

Reorder the terms:
100x + 4x2 = -600

Solving
100x + 4x2 = -600

Solving for variable 'x'.

Reorder the terms:
600 + 100x + 4x2 = -600 + 600

Combine like terms: -600 + 600 = 0
600 + 100x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(150 + 25x + x2) = 0

Factor a trinomial.
4((15 + x)(10 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 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 + x = 0 + -15

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

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

Simplifying
x = -15
Subproblem 2
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
Solution
x = {-15, -10}