7t(2t+5)-3t(3t+1)=

Solution for 7t(2t+5)-3t(3t+1)= equation:

Simplifying
7t(2t + 5) + -3t(3t + 1) = 0

Reorder the terms:
7t(5 + 2t) + -3t(3t + 1) = 0
(5 * 7t + 2t * 7t) + -3t(3t + 1) = 0
(35t + 14t2) + -3t(3t + 1) = 0

Reorder the terms:
35t + 14t2 + -3t(1 + 3t) = 0
35t + 14t2 + (1 * -3t + 3t * -3t) = 0
35t + 14t2 + (-3t + -9t2) = 0

Reorder the terms:
35t + -3t + 14t2 + -9t2 = 0

Combine like terms: 35t + -3t = 32t
32t + 14t2 + -9t2 = 0

Combine like terms: 14t2 + -9t2 = 5t2
32t + 5t2 = 0

Solving
32t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(32 + 5t) = 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 '(32 + 5t)' equal to zero and attempt to solve:

Simplifying
32 + 5t = 0

Solving
32 + 5t = 0

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

Add '-32' to each side of the equation.
32 + -32 + 5t = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 5t = 0 + -32
5t = 0 + -32

Combine like terms: 0 + -32 = -32
5t = -32

Divide each side by '5'.
t = -6.4

Simplifying
t = -6.4
Solution
t = {0, -6.4}