0=-16t(t-9)(t+9)

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Solution for 0=-16t(t-9)(t+9) equation:


Simplifying
0 = -16t(t + -9)(t + 9)

Reorder the terms:
0 = -16t(-9 + t)(t + 9)

Reorder the terms:
0 = -16t(-9 + t)(9 + t)

Multiply (-9 + t) * (9 + t)
0 = -16t(-9(9 + t) + t(9 + t))
0 = -16t((9 * -9 + t * -9) + t(9 + t))
0 = -16t((-81 + -9t) + t(9 + t))
0 = -16t(-81 + -9t + (9 * t + t * t))
0 = -16t(-81 + -9t + (9t + t2))

Combine like terms: -9t + 9t = 0
0 = -16t(-81 + 0 + t2)
0 = -16t(-81 + t2)
0 = (-81 * -16t + t2 * -16t)
0 = (1296t + -16t3)

Solving
0 = 1296t + -16t3

Solving for variable 't'.
Remove the zero:
-1296t + 16t3 = 1296t + -16t3 + -1296t + 16t3

Reorder the terms:
-1296t + 16t3 = 1296t + -1296t + -16t3 + 16t3

Combine like terms: 1296t + -1296t = 0
-1296t + 16t3 = 0 + -16t3 + 16t3
-1296t + 16t3 = -16t3 + 16t3

Combine like terms: -16t3 + 16t3 = 0
-1296t + 16t3 = 0

Factor out the Greatest Common Factor (GCF), '16t'.
16t(-81 + t2) = 0

Factor a difference between two squares.
16t((9 + t)(-9 + t)) = 0

Ignore the factor 16.

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 '(9 + t)' equal to zero and attempt to solve: Simplifying 9 + t = 0 Solving 9 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + t = 0 + -9 t = 0 + -9 Combine like terms: 0 + -9 = -9 t = -9 Simplifying t = -9

Subproblem 3

Set the factor '(-9 + t)' equal to zero and attempt to solve: Simplifying -9 + t = 0 Solving -9 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + t = 0 + 9 t = 0 + 9 Combine like terms: 0 + 9 = 9 t = 9 Simplifying t = 9

Solution

t = {0, -9, 9}

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