6=2t+4t^2

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

Simplifying
6 = 2t + 4t2

Solving
6 = 2t + 4t2

Solving for variable 't'.

Reorder the terms:
6 + -2t + -4t2 = 2t + -2t + 4t2 + -4t2

Combine like terms: 2t + -2t = 0
6 + -2t + -4t2 = 0 + 4t2 + -4t2
6 + -2t + -4t2 = 4t2 + -4t2

Combine like terms: 4t2 + -4t2 = 0
6 + -2t + -4t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -1t + -2t2) = 0

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

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

Simplifying
1 + -1t = 0

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

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

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

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

Simplifying
t = 1
Subproblem 2
Set the factor '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

Solving
3 + 2t = 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 + 2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2t = 0 + -3
2t = 0 + -3

Combine like terms: 0 + -3 = -3
2t = -3

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Solution
t = {1, -1.5}