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

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

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

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

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

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

Combine like terms: -6t + 10t = 4t
2(-10 + 4t + 6t2) = 0
(-10 * 2 + 4t * 2 + 6t2 * 2) = 0
(-20 + 8t + 12t2) = 0

Solving
-20 + 8t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 2t + 3t2) = 0

Factor a trinomial.
4((-5 + -3t)(1 + -1t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -3t)' equal to zero and attempt to solve:

Simplifying
-5 + -3t = 0

Solving
-5 + -3t = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3t = 0 + 5

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

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

Divide each side by '-3'.
t = -1.666666667

Simplifying
t = -1.666666667
Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 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 + -1t = 0 + -1

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

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

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

Simplifying
t = 1
Solution
t = {-1.666666667, 1}