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

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


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

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

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

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

Combine like terms: 4t + -5t = -1t
t(-20 + -1t + t2) = 0
(-20 * t + -1t * t + t2 * t) = 0
(-20t + -1t2 + t3) = 0

Solving
-20t + -1t2 + t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-20 + -1t + t2) = 0

Factor a trinomial.
t((-4 + -1t)(5 + -1t)) = 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 '(-4 + -1t)' equal to zero and attempt to solve:

Simplifying
-4 + -1t = 0

Solving
-4 + -1t = 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 + -1t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1t = 0 + 4
-1t = 0 + 4

Combine like terms: 0 + 4 = 4
-1t = 4

Divide each side by '-1'.
t = -4

Simplifying
t = -4

Subproblem 3
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {0, -4, 5}

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