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

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

Simplifying
2t(4t + -5) + (-5t2) = 0

Reorder the terms:
2t(-5 + 4t) + (-5t2) = 0
(-5 * 2t + 4t * 2t) + (-5t2) = 0
(-10t + 8t2) + (-5t2) = 0

Combine like terms: 8t2 + (-5t2) = 3t2
-10t + 3t2 = 0

Solving
-10t + 3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-10 + 3t) = 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 '(-10 + 3t)' equal to zero and attempt to solve:

Simplifying
-10 + 3t = 0

Solving
-10 + 3t = 0

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

Add '10' to each side of the equation.
-10 + 10 + 3t = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3t = 0 + 10
3t = 0 + 10

Combine like terms: 0 + 10 = 10
3t = 10

Divide each side by '3'.
t = 3.333333333

Simplifying
t = 3.333333333
Solution
t = {0, 3.333333333}