3t(t-2)=4-2t

Solution for 3t(t-2)=4-2t equation:

Simplifying
3t(t + -2) = 4 + -2t

Reorder the terms:
3t(-2 + t) = 4 + -2t
(-2 * 3t + t * 3t) = 4 + -2t
(-6t + 3t2) = 4 + -2t

Solving
-6t + 3t2 = 4 + -2t

Solving for variable 't'.

Reorder the terms:
-4 + -6t + 2t + 3t2 = 4 + -2t + -4 + 2t

Combine like terms: -6t + 2t = -4t
-4 + -4t + 3t2 = 4 + -2t + -4 + 2t

Reorder the terms:
-4 + -4t + 3t2 = 4 + -4 + -2t + 2t

Combine like terms: 4 + -4 = 0
-4 + -4t + 3t2 = 0 + -2t + 2t
-4 + -4t + 3t2 = -2t + 2t

Combine like terms: -2t + 2t = 0
-4 + -4t + 3t2 = 0

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

Subproblem 1
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
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 = {-0.6666666667, 2}