t^3(t-7)(t+8)=0

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Solution for t^3(t-7)(t+8)=0 equation: 


Simplifying
t3(t + -7)(t + 8) = 0

Reorder the terms:
t3(-7 + t)(t + 8) = 0

Reorder the terms:
t3(-7 + t)(8 + t) = 0

Multiply (-7 + t) * (8 + t)
t3(-7(8 + t) + t(8 + t)) = 0
t3((8 * -7 + t * -7) + t(8 + t)) = 0
t3((-56 + -7t) + t(8 + t)) = 0
t3(-56 + -7t + (8 * t + t * t)) = 0
t3(-56 + -7t + (8t + t2)) = 0

Combine like terms: -7t + 8t = 1t
t3(-56 + 1t + t2) = 0
(-56 * t3 + 1t * t3 + t2 * t3) = 0
(-56t3 + 1t4 + t5) = 0

Solving
-56t3 + 1t4 + t5 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't3'.
t3(-56 + t + t2) = 0

Factor a trinomial.
t3((-8 + -1t)(7 + -1t)) = 0


Subproblem 1
Set the factor 't3' equal to zero and attempt to solve:

Simplifying
t3 = 0

Solving
t3 = 0

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

Simplifying
t3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-8 + -1t)' equal to zero and attempt to solve:

Simplifying
-8 + -1t = 0

Solving
-8 + -1t = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1t = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1t = 0 + 8
-1t = 0 + 8

Combine like terms: 0 + 8 = 8
-1t = 8

Divide each side by '-1'.
t = -8

Simplifying
t = -8

Subproblem 3
Set the factor '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Solution
t = {-8, 7}

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