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

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

Simplifying
2t2 + (3 + 5t)(4t) = 0

Remove parenthesis around (4t)
2t2 + (3 + 5t) * 4t = 0

Reorder the terms for easier multiplication:
2t2 + 4t(3 + 5t) = 0
2t2 + (3 * 4t + 5t * 4t) = 0
2t2 + (12t + 20t2) = 0

Reorder the terms:
12t + 2t2 + 20t2 = 0

Combine like terms: 2t2 + 20t2 = 22t2
12t + 22t2 = 0

Solving
12t + 22t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2t'.
2t(6 + 11t) = 0

Ignore the factor 2.
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 '(6 + 11t)' equal to zero and attempt to solve:

Simplifying
6 + 11t = 0

Solving
6 + 11t = 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 + 11t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 11t = 0 + -6
11t = 0 + -6

Combine like terms: 0 + -6 = -6
11t = -6

Divide each side by '11'.
t = -0.5454545455

Simplifying
t = -0.5454545455
Solution
t = {0, -0.5454545455}