0=12t^2+40t-32

Solution for 0=12t^2+40t-32 equation:

Simplifying
0 = 12t2 + 40t + -32

Reorder the terms:
0 = -32 + 40t + 12t2

Solving
0 = -32 + 40t + 12t2

Solving for variable 't'.

Combine like terms: 0 + 32 = 32
32 + -40t + -12t2 = -32 + 40t + 12t2 + 32 + -40t + -12t2

Reorder the terms:
32 + -40t + -12t2 = -32 + 32 + 40t + -40t + 12t2 + -12t2

Combine like terms: -32 + 32 = 0
32 + -40t + -12t2 = 0 + 40t + -40t + 12t2 + -12t2
32 + -40t + -12t2 = 40t + -40t + 12t2 + -12t2

Combine like terms: 40t + -40t = 0
32 + -40t + -12t2 = 0 + 12t2 + -12t2
32 + -40t + -12t2 = 12t2 + -12t2

Combine like terms: 12t2 + -12t2 = 0
32 + -40t + -12t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -10t + -3t2) = 0

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

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

Simplifying
2 + -3t = 0

Solving
2 + -3t = 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 + -3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3t = 0 + -2
-3t = 0 + -2

Combine like terms: 0 + -2 = -2
-3t = -2

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667
Subproblem 2
Set the factor '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

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

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

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

Simplifying
t = -4
Solution
t = {0.6666666667, -4}