t(t+4)=12

Solution for t(t+4)=12 equation:

Simplifying
t(t + 4) = 12

Reorder the terms:
t(4 + t) = 12
(4 * t + t * t) = 12
(4t + t2) = 12

Solving
4t + t2 = 12

Solving for variable 't'.

Reorder the terms:
-12 + 4t + t2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 4t + t2 = 0

Factor a trinomial.
(-6 + -1t)(2 + -1t) = 0

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

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 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 + -1t = 0 + 6

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

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

Divide each side by '-1'.
t = -6

Simplifying
t = -6
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 = {-6, 2}