t(t+5)(t-12)=0

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Solution for t(t+5)(t-12)=0 equation: 


Simplifying
t(t + 5)(t + -12) = 0

Reorder the terms:
t(5 + t)(t + -12) = 0

Reorder the terms:
t(5 + t)(-12 + t) = 0

Multiply (5 + t) * (-12 + t)
t(5(-12 + t) + t(-12 + t)) = 0
t((-12 * 5 + t * 5) + t(-12 + t)) = 0
t((-60 + 5t) + t(-12 + t)) = 0
t(-60 + 5t + (-12 * t + t * t)) = 0
t(-60 + 5t + (-12t + t2)) = 0

Combine like terms: 5t + -12t = -7t
t(-60 + -7t + t2) = 0
(-60 * t + -7t * t + t2 * t) = 0
(-60t + -7t2 + t3) = 0

Solving
-60t + -7t2 + t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-60 + -7t + t2) = 0

Factor a trinomial.
t((-5 + -1t)(12 + -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 '(-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

Subproblem 3
Set the factor '(12 + -1t)' equal to zero and attempt to solve:

Simplifying
12 + -1t = 0

Solving
12 + -1t = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1t = 0 + -12
-1t = 0 + -12

Combine like terms: 0 + -12 = -12
-1t = -12

Divide each side by '-1'.
t = 12

Simplifying
t = 12
Solution
t = {0, -5, 12}

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