t(2t+4)=48

Solution for t(2t+4)=48 equation:

Simplifying
t(2t + 4) = 48

Reorder the terms:
t(4 + 2t) = 48
(4 * t + 2t * t) = 48
(4t + 2t2) = 48

Solving
4t + 2t2 = 48

Solving for variable 't'.

Reorder the terms:
-48 + 4t + 2t2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 4t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 2t + t2) = 0

Factor a trinomial.
2((-6 + -1t)(4 + -1t)) = 0

Ignore the factor 2.
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 '(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
Solution
t = {-6, 4}