t(7+t)=3(2t+4)

Solution for t(7+t)=3(2t+4) equation:

Simplifying
t(7 + t) = 3(2t + 4)
(7 * t + t * t) = 3(2t + 4)
(7t + t2) = 3(2t + 4)

Reorder the terms:
7t + t2 = 3(4 + 2t)
7t + t2 = (4 * 3 + 2t * 3)
7t + t2 = (12 + 6t)

Solving
7t + t2 = 12 + 6t

Solving for variable 't'.

Reorder the terms:
-12 + 7t + -6t + t2 = 12 + 6t + -12 + -6t

Combine like terms: 7t + -6t = 1t
-12 + 1t + t2 = 12 + 6t + -12 + -6t

Reorder the terms:
-12 + 1t + t2 = 12 + -12 + 6t + -6t

Combine like terms: 12 + -12 = 0
-12 + 1t + t2 = 0 + 6t + -6t
-12 + 1t + t2 = 6t + -6t

Combine like terms: 6t + -6t = 0
-12 + 1t + t2 = 0

Factor a trinomial.
(-4 + -1t)(3 + -1t) = 0

Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve:

Simplifying
-4 + -1t = 0

Solving
-4 + -1t = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1t = 0 + 4
-1t = 0 + 4

Combine like terms: 0 + 4 = 4
-1t = 4

Divide each side by '-1'.
t = -4

Simplifying
t = -4
Subproblem 2
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
Solution
t = {-4, 3}