(5t+3)(2t-6)=0

Solution for (5t+3)(2t-6)=0 equation:

Simplifying
(5t + 3)(2t + -6) = 0

Reorder the terms:
(3 + 5t)(2t + -6) = 0

Reorder the terms:
(3 + 5t)(-6 + 2t) = 0

Multiply (3 + 5t) * (-6 + 2t)
(3(-6 + 2t) + 5t * (-6 + 2t)) = 0
((-6 * 3 + 2t * 3) + 5t * (-6 + 2t)) = 0
((-18 + 6t) + 5t * (-6 + 2t)) = 0
(-18 + 6t + (-6 * 5t + 2t * 5t)) = 0
(-18 + 6t + (-30t + 10t2)) = 0

Combine like terms: 6t + -30t = -24t
(-18 + -24t + 10t2) = 0

Solving
-18 + -24t + 10t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -12t + 5t2) = 0

Factor a trinomial.
2((-3 + -5t)(3 + -1t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -5t)' equal to zero and attempt to solve:

Simplifying
-3 + -5t = 0

Solving
-3 + -5t = 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 + -5t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5t = 0 + 3
-5t = 0 + 3

Combine like terms: 0 + 3 = 3
-5t = 3

Divide each side by '-5'.
t = -0.6

Simplifying
t = -0.6
Subproblem 2
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
Solution
t = {-0.6, 3}