(3t-t)(4-3t)=7t

Solution for (3t-t)(4-3t)=7t equation:

Simplifying
(3t + -1t)(4 + -3t) = 7t

Combine like terms: 3t + -1t = 2t
(2t)(4 + -3t) = 7t

Remove parenthesis around (2t)
2t(4 + -3t) = 7t
(4 * 2t + -3t * 2t) = 7t
(8t + -6t2) = 7t

Solving
8t + -6t2 = 7t

Solving for variable 't'.

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

Combine like terms: 8t + -7t = 1t
1t + -6t2 = 7t + -7t

Combine like terms: 7t + -7t = 0
1t + -6t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(1 + -6t) = 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 '(1 + -6t)' equal to zero and attempt to solve:

Simplifying
1 + -6t = 0

Solving
1 + -6t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -6t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6t = 0 + -1
-6t = 0 + -1

Combine like terms: 0 + -1 = -1
-6t = -1

Divide each side by '-6'.
t = 0.1666666667

Simplifying
t = 0.1666666667
Solution
t = {0, 0.1666666667}