3t^2+12t-31=5

Solution for 3t^2+12t-31=5 equation:

Simplifying
3t2 + 12t + -31 = 5

Reorder the terms:
-31 + 12t + 3t2 = 5

Solving
-31 + 12t + 3t2 = 5

Solving for variable 't'.

Reorder the terms:
-31 + -5 + 12t + 3t2 = 5 + -5

Combine like terms: -31 + -5 = -36
-36 + 12t + 3t2 = 5 + -5

Combine like terms: 5 + -5 = 0
-36 + 12t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 4t + t2) = 0

Factor a trinomial.
3((-6 + -1t)(2 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-6, 2}