-4t(5t+3)(3t-5)=0

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Solution for -4t(5t+3)(3t-5)=0 equation: 


Simplifying
-4t(5t + 3)(3t + -5) = 0

Reorder the terms:
-4t(3 + 5t)(3t + -5) = 0

Reorder the terms:
-4t(3 + 5t)(-5 + 3t) = 0

Multiply (3 + 5t) * (-5 + 3t)
-4t(3(-5 + 3t) + 5t * (-5 + 3t)) = 0
-4t((-5 * 3 + 3t * 3) + 5t * (-5 + 3t)) = 0
-4t((-15 + 9t) + 5t * (-5 + 3t)) = 0
-4t(-15 + 9t + (-5 * 5t + 3t * 5t)) = 0
-4t(-15 + 9t + (-25t + 15t2)) = 0

Combine like terms: 9t + -25t = -16t
-4t(-15 + -16t + 15t2) = 0
(-15 * -4t + -16t * -4t + 15t2 * -4t) = 0
(60t + 64t2 + -60t3) = 0

Solving
60t + 64t2 + -60t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4t'.
4t(15 + 16t + -15t2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0

Subproblem 2
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 3
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
Solution
t = {0, 1.666666667, -0.6}

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