t(2t+3)=2(t+3)

Solution for t(2t+3)=2(t+3) equation:

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

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

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

Solving
3t + 2t2 = 6 + 2t

Solving for variable 't'.

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

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

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

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

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

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

Subproblem 1
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
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 = {-2, 1.5}