(t^2-12)(t-3)=(t+18)(t+2)

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Solution for (t^2-12)(t-3)=(t+18)(t+2) equation: 


Simplifying
(t2 + -12)(t + -3) = (t + 18)(t + 2)

Reorder the terms:
(-12 + t2)(t + -3) = (t + 18)(t + 2)

Reorder the terms:
(-12 + t2)(-3 + t) = (t + 18)(t + 2)

Multiply (-12 + t2) * (-3 + t)
(-12(-3 + t) + t2(-3 + t)) = (t + 18)(t + 2)
((-3 * -12 + t * -12) + t2(-3 + t)) = (t + 18)(t + 2)
((36 + -12t) + t2(-3 + t)) = (t + 18)(t + 2)
(36 + -12t + (-3 * t2 + t * t2)) = (t + 18)(t + 2)
(36 + -12t + (-3t2 + t3)) = (t + 18)(t + 2)
(36 + -12t + -3t2 + t3) = (t + 18)(t + 2)

Reorder the terms:
36 + -12t + -3t2 + t3 = (18 + t)(t + 2)

Reorder the terms:
36 + -12t + -3t2 + t3 = (18 + t)(2 + t)

Multiply (18 + t) * (2 + t)
36 + -12t + -3t2 + t3 = (18(2 + t) + t(2 + t))
36 + -12t + -3t2 + t3 = ((2 * 18 + t * 18) + t(2 + t))
36 + -12t + -3t2 + t3 = ((36 + 18t) + t(2 + t))
36 + -12t + -3t2 + t3 = (36 + 18t + (2 * t + t * t))
36 + -12t + -3t2 + t3 = (36 + 18t + (2t + t2))

Combine like terms: 18t + 2t = 20t
36 + -12t + -3t2 + t3 = (36 + 20t + t2)

Add '-36' to each side of the equation.
36 + -12t + -3t2 + -36 + t3 = 36 + 20t + -36 + t2

Reorder the terms:
36 + -36 + -12t + -3t2 + t3 = 36 + 20t + -36 + t2

Combine like terms: 36 + -36 = 0
0 + -12t + -3t2 + t3 = 36 + 20t + -36 + t2
-12t + -3t2 + t3 = 36 + 20t + -36 + t2

Reorder the terms:
-12t + -3t2 + t3 = 36 + -36 + 20t + t2

Combine like terms: 36 + -36 = 0
-12t + -3t2 + t3 = 0 + 20t + t2
-12t + -3t2 + t3 = 20t + t2

Solving
-12t + -3t2 + t3 = 20t + t2

Solving for variable 't'.

Reorder the terms:
-12t + -20t + -3t2 + -1t2 + t3 = 20t + t2 + -20t + -1t2

Combine like terms: -12t + -20t = -32t
-32t + -3t2 + -1t2 + t3 = 20t + t2 + -20t + -1t2

Combine like terms: -3t2 + -1t2 = -4t2
-32t + -4t2 + t3 = 20t + t2 + -20t + -1t2

Reorder the terms:
-32t + -4t2 + t3 = 20t + -20t + t2 + -1t2

Combine like terms: 20t + -20t = 0
-32t + -4t2 + t3 = 0 + t2 + -1t2
-32t + -4t2 + t3 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-32t + -4t2 + t3 = 0

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

Factor a trinomial.
t((-4 + -1t)(8 + -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 '(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
Solution
t = {0, -4, 8}

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