(7t-4)(3t+6)=0

Solution for (7t-4)(3t+6)=0 equation:

Simplifying
(7t + -4)(3t + 6) = 0

Reorder the terms:
(-4 + 7t)(3t + 6) = 0

Reorder the terms:
(-4 + 7t)(6 + 3t) = 0

Multiply (-4 + 7t) * (6 + 3t)
(-4(6 + 3t) + 7t * (6 + 3t)) = 0
((6 * -4 + 3t * -4) + 7t * (6 + 3t)) = 0
((-24 + -12t) + 7t * (6 + 3t)) = 0
(-24 + -12t + (6 * 7t + 3t * 7t)) = 0
(-24 + -12t + (42t + 21t2)) = 0

Combine like terms: -12t + 42t = 30t
(-24 + 30t + 21t2) = 0

Solving
-24 + 30t + 21t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 10t + 7t2) = 0

Factor a trinomial.
3((-2 + -1t)(4 + -7t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve:

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

Simplifying
t = -2
Subproblem 2
Set the factor '(4 + -7t)' equal to zero and attempt to solve:

Simplifying
4 + -7t = 0

Solving
4 + -7t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7t = 0 + -4
-7t = 0 + -4

Combine like terms: 0 + -4 = -4
-7t = -4

Divide each side by '-7'.
t = 0.5714285714

Simplifying
t = 0.5714285714
Solution
t = {-2, 0.5714285714}