7t(t-4)-2t(8t-4t+3)=0

Solution for 7t(t-4)-2t(8t-4t+3)=0 equation:

Simplifying
7t(t + -4) + -2t(8t + -4t + 3) = 0

Reorder the terms:
7t(-4 + t) + -2t(8t + -4t + 3) = 0
(-4 * 7t + t * 7t) + -2t(8t + -4t + 3) = 0
(-28t + 7t2) + -2t(8t + -4t + 3) = 0

Reorder the terms:
-28t + 7t2 + -2t(3 + 8t + -4t) = 0

Combine like terms: 8t + -4t = 4t
-28t + 7t2 + -2t(3 + 4t) = 0
-28t + 7t2 + (3 * -2t + 4t * -2t) = 0
-28t + 7t2 + (-6t + -8t2) = 0

Reorder the terms:
-28t + -6t + 7t2 + -8t2 = 0

Combine like terms: -28t + -6t = -34t
-34t + 7t2 + -8t2 = 0

Combine like terms: 7t2 + -8t2 = -1t2
-34t + -1t2 = 0

Solving
-34t + -1t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-1t'.
-1t(34 + t) = 0

Ignore the factor -1.
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 '(34 + t)' equal to zero and attempt to solve:

Simplifying
34 + t = 0

Solving
34 + t = 0

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

Add '-34' to each side of the equation.
34 + -34 + t = 0 + -34

Combine like terms: 34 + -34 = 0
0 + t = 0 + -34
t = 0 + -34

Combine like terms: 0 + -34 = -34
t = -34

Simplifying
t = -34
Solution
t = {0, -34}