0=12t^2+7t+1

Solution for 0=12t^2+7t+1 equation:

Simplifying
0 = 12t2 + 7t + 1

Reorder the terms:
0 = 1 + 7t + 12t2

Solving
0 = 1 + 7t + 12t2

Solving for variable 't'.

Combine like terms: 0 + -1 = -1
-1 + -7t + -12t2 = 1 + 7t + 12t2 + -1 + -7t + -12t2

Reorder the terms:
-1 + -7t + -12t2 = 1 + -1 + 7t + -7t + 12t2 + -12t2

Combine like terms: 1 + -1 = 0
-1 + -7t + -12t2 = 0 + 7t + -7t + 12t2 + -12t2
-1 + -7t + -12t2 = 7t + -7t + 12t2 + -12t2

Combine like terms: 7t + -7t = 0
-1 + -7t + -12t2 = 0 + 12t2 + -12t2
-1 + -7t + -12t2 = 12t2 + -12t2

Combine like terms: 12t2 + -12t2 = 0
-1 + -7t + -12t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 7t + 12t2) = 0

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

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

Simplifying
1 + 3t = 0

Solving
1 + 3t = 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 + 3t = 0 + -1

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

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

Divide each side by '3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
Subproblem 2
Set the factor '(1 + 4t)' equal to zero and attempt to solve:

Simplifying
1 + 4t = 0

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

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

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

Divide each side by '4'.
t = -0.25

Simplifying
t = -0.25
Solution
t = {-0.3333333333, -0.25}