8(t^2+t-12)=0

Solution for 8(t^2+t-12)=0 equation:

Simplifying
8(t2 + t + -12) = 0

Reorder the terms:
8(-12 + t + t2) = 0
(-12 * 8 + t * 8 + t2 * 8) = 0
(-96 + 8t + 8t2) = 0

Solving
-96 + 8t + 8t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-12 + t + t2) = 0

Factor a trinomial.
8((-4 + -1t)(3 + -1t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve:

Simplifying
-4 + -1t = 0

Solving
-4 + -1t = 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 + -1t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1t = 0 + 4
-1t = 0 + 4

Combine like terms: 0 + 4 = 4
-1t = 4

Divide each side by '-1'.
t = -4

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

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-4, 3}