0=6t^2+14t+4

Solution for 0=6t^2+14t+4 equation:

Simplifying
0 = 6t2 + 14t + 4

Reorder the terms:
0 = 4 + 14t + 6t2

Solving
0 = 4 + 14t + 6t2

Solving for variable 't'.

Combine like terms: 0 + -4 = -4
-4 + -14t + -6t2 = 4 + 14t + 6t2 + -4 + -14t + -6t2

Reorder the terms:
-4 + -14t + -6t2 = 4 + -4 + 14t + -14t + 6t2 + -6t2

Combine like terms: 4 + -4 = 0
-4 + -14t + -6t2 = 0 + 14t + -14t + 6t2 + -6t2
-4 + -14t + -6t2 = 14t + -14t + 6t2 + -6t2

Combine like terms: 14t + -14t = 0
-4 + -14t + -6t2 = 0 + 6t2 + -6t2
-4 + -14t + -6t2 = 6t2 + -6t2

Combine like terms: 6t2 + -6t2 = 0
-4 + -14t + -6t2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(2 + 7t + 3t2) = 0

Factor a trinomial.
-2((2 + t)(1 + 3t)) = 0

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

Simplifying
2 + t = 0

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

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

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

Simplifying
t = -2
Subproblem 2
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
Solution
t = {-2, -0.3333333333}