12t^2+8t-32=

Solution for 12t^2+8t-32= equation:

Simplifying
12t2 + 8t + -32 = 0

Reorder the terms:
-32 + 8t + 12t2 = 0

Solving
-32 + 8t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 2t + 3t2) = 0

Factor a trinomial.
4((-2 + -1t)(4 + -3t)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -3t)' equal to zero and attempt to solve:

Simplifying
4 + -3t = 0

Solving
4 + -3t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3t = 0 + -4

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

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

Divide each side by '-3'.
t = 1.333333333

Simplifying
t = 1.333333333
Solution
t = {-2, 1.333333333}