12t^2+19t-21=0

Solution for 12t^2+19t-21=0 equation:

Simplifying
12t2 + 19t + -21 = 0

Reorder the terms:
-21 + 19t + 12t2 = 0

Solving
-21 + 19t + 12t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-7 + -3t)(3 + -4t) = 0

Subproblem 1
Set the factor '(-7 + -3t)' equal to zero and attempt to solve:

Simplifying
-7 + -3t = 0

Solving
-7 + -3t = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3t = 0 + 7
-3t = 0 + 7

Combine like terms: 0 + 7 = 7
-3t = 7

Divide each side by '-3'.
t = -2.333333333

Simplifying
t = -2.333333333
Subproblem 2
Set the factor '(3 + -4t)' equal to zero and attempt to solve:

Simplifying
3 + -4t = 0

Solving
3 + -4t = 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 + -4t = 0 + -3

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

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

Divide each side by '-4'.
t = 0.75

Simplifying
t = 0.75
Solution
t = {-2.333333333, 0.75}