4(4t+5)(2t+3)=

Solution for 4(4t+5)(2t+3)= equation:

Simplifying
4(4t + 5)(2t + 3) = 0

Reorder the terms:
4(5 + 4t)(2t + 3) = 0

Reorder the terms:
4(5 + 4t)(3 + 2t) = 0

Multiply (5 + 4t) * (3 + 2t)
4(5(3 + 2t) + 4t * (3 + 2t)) = 0
4((3 * 5 + 2t * 5) + 4t * (3 + 2t)) = 0
4((15 + 10t) + 4t * (3 + 2t)) = 0
4(15 + 10t + (3 * 4t + 2t * 4t)) = 0
4(15 + 10t + (12t + 8t2)) = 0

Combine like terms: 10t + 12t = 22t
4(15 + 22t + 8t2) = 0
(15 * 4 + 22t * 4 + 8t2 * 4) = 0
(60 + 88t + 32t2) = 0

Solving
60 + 88t + 32t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + 22t + 8t2) = 0

Factor a trinomial.
4((3 + 2t)(5 + 4t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

Solving
3 + 2t = 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 + 2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2t = 0 + -3
2t = 0 + -3

Combine like terms: 0 + -3 = -3
2t = -3

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Subproblem 2
Set the factor '(5 + 4t)' equal to zero and attempt to solve:

Simplifying
5 + 4t = 0

Solving
5 + 4t = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4t = 0 + -5
4t = 0 + -5

Combine like terms: 0 + -5 = -5
4t = -5

Divide each side by '4'.
t = -1.25

Simplifying
t = -1.25
Solution
t = {-1.5, -1.25}