48s^2+84s=-36

Solution for 48s^2+84s=-36 equation:

Simplifying
48s2 + 84s = -36

Reorder the terms:
84s + 48s2 = -36

Solving
84s + 48s2 = -36

Solving for variable 's'.

Reorder the terms:
36 + 84s + 48s2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + 84s + 48s2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(3 + 7s + 4s2) = 0

Factor a trinomial.
12((1 + s)(3 + 4s)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(1 + s)' equal to zero and attempt to solve:

Simplifying
1 + s = 0

Solving
1 + s = 0

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

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

Combine like terms: 1 + -1 = 0
0 + s = 0 + -1
s = 0 + -1

Combine like terms: 0 + -1 = -1
s = -1

Simplifying
s = -1
Subproblem 2
Set the factor '(3 + 4s)' equal to zero and attempt to solve:

Simplifying
3 + 4s = 0

Solving
3 + 4s = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4s = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4s = 0 + -3
4s = 0 + -3

Combine like terms: 0 + -3 = -3
4s = -3

Divide each side by '4'.
s = -0.75

Simplifying
s = -0.75
Solution
s = {-1, -0.75}