t(8-3t)(4+t)=0

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Solution for t(8-3t)(4+t)=0 equation: 


Simplifying
t(8 + -3t)(4 + t) = 0

Multiply (8 + -3t) * (4 + t)
t(8(4 + t) + -3t * (4 + t)) = 0
t((4 * 8 + t * 8) + -3t * (4 + t)) = 0
t((32 + 8t) + -3t * (4 + t)) = 0
t(32 + 8t + (4 * -3t + t * -3t)) = 0
t(32 + 8t + (-12t + -3t2)) = 0

Combine like terms: 8t + -12t = -4t
t(32 + -4t + -3t2) = 0
(32 * t + -4t * t + -3t2 * t) = 0
(32t + -4t2 + -3t3) = 0

Solving
32t + -4t2 + -3t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(32 + -4t + -3t2) = 0

Factor a trinomial.
t((8 + -3t)(4 + t)) = 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 '(8 + -3t)' equal to zero and attempt to solve:

Simplifying
8 + -3t = 0

Solving
8 + -3t = 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 + -3t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3t = 0 + -8
-3t = 0 + -8

Combine like terms: 0 + -8 = -8
-3t = -8

Divide each side by '-3'.
t = 2.666666667

Simplifying
t = 2.666666667

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

Simplifying
4 + t = 0

Solving
4 + t = 0

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

Add '-4' to each side of the equation.
4 + -4 + t = 0 + -4

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

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

Simplifying
t = -4
Solution
t = {0, 2.666666667, -4}

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