2(t+3)=t(t+7)

Solution for 2(t+3)=t(t+7) equation:

Simplifying
2(t + 3) = t(t + 7)

Reorder the terms:
2(3 + t) = t(t + 7)
(3 * 2 + t * 2) = t(t + 7)
(6 + 2t) = t(t + 7)

Reorder the terms:
6 + 2t = t(7 + t)
6 + 2t = (7 * t + t * t)
6 + 2t = (7t + t2)

Solving
6 + 2t = 7t + t2

Solving for variable 't'.

Combine like terms: 2t + -7t = -5t
6 + -5t + -1t2 = 7t + t2 + -7t + -1t2

Reorder the terms:
6 + -5t + -1t2 = 7t + -7t + t2 + -1t2

Combine like terms: 7t + -7t = 0
6 + -5t + -1t2 = 0 + t2 + -1t2
6 + -5t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
6 + -5t + -1t2 = 0

Factor a trinomial.
(1 + -1t)(6 + t) = 0

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

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1t = 0 + -1

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

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

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

Simplifying
t = 1
Subproblem 2
Set the factor '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 0

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

Add '-6' to each side of the equation.
6 + -6 + t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + t = 0 + -6
t = 0 + -6

Combine like terms: 0 + -6 = -6
t = -6

Simplifying
t = -6
Solution
t = {1, -6}