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

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

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

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

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

Multiply (-4 + 2t) * (3 + t)
(-4(3 + t) + 2t * (3 + t)) = 0
((3 * -4 + t * -4) + 2t * (3 + t)) = 0
((-12 + -4t) + 2t * (3 + t)) = 0
(-12 + -4t + (3 * 2t + t * 2t)) = 0
(-12 + -4t + (6t + 2t2)) = 0

Combine like terms: -4t + 6t = 2t
(-12 + 2t + 2t2) = 0

Solving
-12 + 2t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + t + t2) = 0

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

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

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1t = 0 + 3
-1t = 0 + 3

Combine like terms: 0 + 3 = 3
-1t = 3

Divide each side by '-1'.
t = -3

Simplifying
t = -3
Subproblem 2
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
Solution
t = {-3, 2}