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

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

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

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

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

Multiply (2 + t) * (-4 + 3t)
(2(-4 + 3t) + t(-4 + 3t)) = 0
((-4 * 2 + 3t * 2) + t(-4 + 3t)) = 0
((-8 + 6t) + t(-4 + 3t)) = 0
(-8 + 6t + (-4 * t + 3t * t)) = 0
(-8 + 6t + (-4t + 3t2)) = 0

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

Solving
-8 + 2t + 3t2 = 0

Solving for variable 't'.

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

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 + -3t)' equal to zero and attempt to solve:

Simplifying
4 + -3t = 0

Solving
4 + -3t = 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 + -3t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3t = 0 + -4
-3t = 0 + -4

Combine like terms: 0 + -4 = -4
-3t = -4

Divide each side by '-3'.
t = 1.333333333

Simplifying
t = 1.333333333
Solution
t = {-2, 1.333333333}