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

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

Simplifying
t(3 + t) = 2(t + 3)
(3 * t + t * t) = 2(t + 3)
(3t + t2) = 2(t + 3)

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

Solving
3t + t2 = 6 + 2t

Solving for variable 't'.

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

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

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

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

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

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

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

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 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 + -1t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1t = 0 + 3
-1t = 0 + 3

Combine like terms: 0 + 3 = 3
-1t = 3

Divide each side by '-1'.
t = -3

Simplifying
t = -3
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 = {-3, 2}