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

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

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

Reorder the terms:
2t(-4 + 3t) + t(2t + 5) = 0
(-4 * 2t + 3t * 2t) + t(2t + 5) = 0
(-8t + 6t2) + t(2t + 5) = 0

Reorder the terms:
-8t + 6t2 + t(5 + 2t) = 0
-8t + 6t2 + (5 * t + 2t * t) = 0
-8t + 6t2 + (5t + 2t2) = 0

Reorder the terms:
-8t + 5t + 6t2 + 2t2 = 0

Combine like terms: -8t + 5t = -3t
-3t + 6t2 + 2t2 = 0

Combine like terms: 6t2 + 2t2 = 8t2
-3t + 8t2 = 0

Solving
-3t + 8t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-3 + 8t) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(-3 + 8t)' equal to zero and attempt to solve:

Simplifying
-3 + 8t = 0

Solving
-3 + 8t = 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 + 8t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 8t = 0 + 3
8t = 0 + 3

Combine like terms: 0 + 3 = 3
8t = 3

Divide each side by '8'.
t = 0.375

Simplifying
t = 0.375
Solution
t = {0, 0.375}