3s^2+6=3s+12

Solution for 3s^2+6=3s+12 equation:

Simplifying
3s2 + 6 = 3s + 12

Reorder the terms:
6 + 3s2 = 3s + 12

Reorder the terms:
6 + 3s2 = 12 + 3s

Solving
6 + 3s2 = 12 + 3s

Solving for variable 's'.

Reorder the terms:
6 + -12 + -3s + 3s2 = 12 + 3s + -12 + -3s

Combine like terms: 6 + -12 = -6
-6 + -3s + 3s2 = 12 + 3s + -12 + -3s

Reorder the terms:
-6 + -3s + 3s2 = 12 + -12 + 3s + -3s

Combine like terms: 12 + -12 = 0
-6 + -3s + 3s2 = 0 + 3s + -3s
-6 + -3s + 3s2 = 3s + -3s

Combine like terms: 3s + -3s = 0
-6 + -3s + 3s2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -1s + s2) = 0

Factor a trinomial.
3((-1 + -1s)(2 + -1s)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -1s)' equal to zero and attempt to solve:

Simplifying
-1 + -1s = 0

Solving
-1 + -1s = 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 + -1s = 0 + 1

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

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

Divide each side by '-1'.
s = -1

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

Simplifying
2 + -1s = 0

Solving
2 + -1s = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1s = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1s = 0 + -2
-1s = 0 + -2

Combine like terms: 0 + -2 = -2
-1s = -2

Divide each side by '-1'.
s = 2

Simplifying
s = 2
Solution
s = {-1, 2}