3t^2+6t+2=26

Solution for 3t^2+6t+2=26 equation:

Simplifying
3t2 + 6t + 2 = 26

Reorder the terms:
2 + 6t + 3t2 = 26

Solving
2 + 6t + 3t2 = 26

Solving for variable 't'.

Reorder the terms:
2 + -26 + 6t + 3t2 = 26 + -26

Combine like terms: 2 + -26 = -24
-24 + 6t + 3t2 = 26 + -26

Combine like terms: 26 + -26 = 0
-24 + 6t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 2t + t2) = 0

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

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 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 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-4, 2}