(4t-2t)t^2=6t+t^2

Solution for (4t-2t)t^2=6t+t^2 equation:

Simplifying
(4t + -2t) * t2 = 6t + t2

Combine like terms: 4t + -2t = 2t
(2t) * t2 = 6t + t2

Remove parenthesis around (2t)
2t * t2 = 6t + t2

Multiply t * t2
2t3 = 6t + t2

Solving
2t3 = 6t + t2

Solving for variable 't'.

Reorder the terms:
-6t + -1t2 + 2t3 = 6t + t2 + -6t + -1t2

Reorder the terms:
-6t + -1t2 + 2t3 = 6t + -6t + t2 + -1t2

Combine like terms: 6t + -6t = 0
-6t + -1t2 + 2t3 = 0 + t2 + -1t2
-6t + -1t2 + 2t3 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-6t + -1t2 + 2t3 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-6 + -1t + 2t2) = 0

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

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
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
Subproblem 3
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 = {0, -1.5, 2}