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

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

Simplifying
t(7 + t) = 2(t + 7)
(7 * t + t * t) = 2(t + 7)
(7t + t2) = 2(t + 7)

Reorder the terms:
7t + t2 = 2(7 + t)
7t + t2 = (7 * 2 + t * 2)
7t + t2 = (14 + 2t)

Solving
7t + t2 = 14 + 2t

Solving for variable 't'.

Reorder the terms:
-14 + 7t + -2t + t2 = 14 + 2t + -14 + -2t

Combine like terms: 7t + -2t = 5t
-14 + 5t + t2 = 14 + 2t + -14 + -2t

Reorder the terms:
-14 + 5t + t2 = 14 + -14 + 2t + -2t

Combine like terms: 14 + -14 = 0
-14 + 5t + t2 = 0 + 2t + -2t
-14 + 5t + t2 = 2t + -2t

Combine like terms: 2t + -2t = 0
-14 + 5t + t2 = 0

Factor a trinomial.
(-7 + -1t)(2 + -1t) = 0

Subproblem 1
Set the factor '(-7 + -1t)' equal to zero and attempt to solve:

Simplifying
-7 + -1t = 0

Solving
-7 + -1t = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1t = 0 + 7
-1t = 0 + 7

Combine like terms: 0 + 7 = 7
-1t = 7

Divide each side by '-1'.
t = -7

Simplifying
t = -7
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 = {-7, 2}