0=12(t^2-3t-4)

Solution for 0=12(t^2-3t-4) equation:

Simplifying
0 = 12(t2 + -3t + -4)

Reorder the terms:
0 = 12(-4 + -3t + t2)
0 = (-4 * 12 + -3t * 12 + t2 * 12)
0 = (-48 + -36t + 12t2)

Solving
0 = -48 + -36t + 12t2

Solving for variable 't'.

Combine like terms: 0 + 48 = 48
48 + 36t + -12t2 = -48 + -36t + 12t2 + 48 + 36t + -12t2

Reorder the terms:
48 + 36t + -12t2 = -48 + 48 + -36t + 36t + 12t2 + -12t2

Combine like terms: -48 + 48 = 0
48 + 36t + -12t2 = 0 + -36t + 36t + 12t2 + -12t2
48 + 36t + -12t2 = -36t + 36t + 12t2 + -12t2

Combine like terms: -36t + 36t = 0
48 + 36t + -12t2 = 0 + 12t2 + -12t2
48 + 36t + -12t2 = 12t2 + -12t2

Combine like terms: 12t2 + -12t2 = 0
48 + 36t + -12t2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(4 + 3t + -1t2) = 0

Factor a trinomial.
12((4 + -1t)(1 + t)) = 0

Ignore the factor 12.
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 '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

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

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

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

Simplifying
t = -1
Solution
t = {4, -1}