3t^2+10t+6=14

Solution for 3t^2+10t+6=14 equation:

Simplifying
3t2 + 10t + 6 = 14

Reorder the terms:
6 + 10t + 3t2 = 14

Solving
6 + 10t + 3t2 = 14

Solving for variable 't'.

Reorder the terms:
6 + -14 + 10t + 3t2 = 14 + -14

Combine like terms: 6 + -14 = -8
-8 + 10t + 3t2 = 14 + -14

Combine like terms: 14 + -14 = 0
-8 + 10t + 3t2 = 0

Factor a trinomial.
(-4 + -1t)(2 + -3t) = 0

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 '(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
Solution
t = {-4, 0.6666666667}