6t^2=15+27t

Solution for 6t^2=15+27t equation:

Simplifying
6t2 = 15 + 27t

Solving
6t2 = 15 + 27t

Solving for variable 't'.

Reorder the terms:
-15 + -27t + 6t2 = 15 + 27t + -15 + -27t

Reorder the terms:
-15 + -27t + 6t2 = 15 + -15 + 27t + -27t

Combine like terms: 15 + -15 = 0
-15 + -27t + 6t2 = 0 + 27t + -27t
-15 + -27t + 6t2 = 27t + -27t

Combine like terms: 27t + -27t = 0
-15 + -27t + 6t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -9t + 2t2) = 0

Factor a trinomial.
3((-1 + -2t)(5 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -2t)' equal to zero and attempt to solve:

Simplifying
-1 + -2t = 0

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

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

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

Divide each side by '-2'.
t = -0.5

Simplifying
t = -0.5
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-0.5, 5}