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

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


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

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

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

Multiply (5 + 4t) * (-5 + 4t)
t(5(-5 + 4t) + 4t * (-5 + 4t)) = 0
t((-5 * 5 + 4t * 5) + 4t * (-5 + 4t)) = 0
t((-25 + 20t) + 4t * (-5 + 4t)) = 0
t(-25 + 20t + (-5 * 4t + 4t * 4t)) = 0
t(-25 + 20t + (-20t + 16t2)) = 0

Combine like terms: 20t + -20t = 0
t(-25 + 0 + 16t2) = 0
t(-25 + 16t2) = 0
(-25 * t + 16t2 * t) = 0
(-25t + 16t3) = 0

Solving
-25t + 16t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-25 + 16t2) = 0

Factor a difference between two squares.
t((5 + 4t)(-5 + 4t)) = 0


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 + 4t)' equal to zero and attempt to solve:

Simplifying
5 + 4t = 0

Solving
5 + 4t = 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 + 4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4t = 0 + -5
4t = 0 + -5

Combine like terms: 0 + -5 = -5
4t = -5

Divide each side by '4'.
t = -1.25

Simplifying
t = -1.25

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

Simplifying
-5 + 4t = 0

Solving
-5 + 4t = 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 + 4t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 4t = 0 + 5
4t = 0 + 5

Combine like terms: 0 + 5 = 5
4t = 5

Divide each side by '4'.
t = 1.25

Simplifying
t = 1.25
Solution
t = {0, -1.25, 1.25}

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