t(t+2)=48

Solution for t(t+2)=48 equation:

Simplifying
t(t + 2) = 48

Reorder the terms:
t(2 + t) = 48
(2 * t + t * t) = 48
(2t + t2) = 48

Solving
2t + t2 = 48

Solving for variable 't'.

Reorder the terms:
-48 + 2t + t2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 2t + t2 = 0

Factor a trinomial.
(-8 + -1t)(6 + -1t) = 0

Subproblem 1
Set the factor '(-8 + -1t)' equal to zero and attempt to solve:

Simplifying
-8 + -1t = 0

Solving
-8 + -1t = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1t = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1t = 0 + 8
-1t = 0 + 8

Combine like terms: 0 + 8 = 8
-1t = 8

Divide each side by '-1'.
t = -8

Simplifying
t = -8
Subproblem 2
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
Solution
t = {-8, 6}