2t(t-2)=6-3t

Solution for 2t(t-2)=6-3t equation:

Simplifying
2t(t + -2) = 6 + -3t

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

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

Solving for variable 't'.

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

Combine like terms: -4t + 3t = -1t
-6 + -1t + 2t2 = 6 + -3t + -6 + 3t

Reorder the terms:
-6 + -1t + 2t2 = 6 + -6 + -3t + 3t

Combine like terms: 6 + -6 = 0
-6 + -1t + 2t2 = 0 + -3t + 3t
-6 + -1t + 2t2 = -3t + 3t

Combine like terms: -3t + 3t = 0
-6 + -1t + 2t2 = 0

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

Subproblem 1
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 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 = {-1.5, 2}