(t-2)(t-10)(t-18)+360=0

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Solution for (t-2)(t-10)(t-18)+360=0 equation: 


Simplifying
(t + -2)(t + -10)(t + -18) + 360 = 0

Reorder the terms:
(-2 + t)(t + -10)(t + -18) + 360 = 0

Reorder the terms:
(-2 + t)(-10 + t)(t + -18) + 360 = 0

Reorder the terms:
(-2 + t)(-10 + t)(-18 + t) + 360 = 0

Multiply (-2 + t) * (-10 + t)
(-2(-10 + t) + t(-10 + t))(-18 + t) + 360 = 0
((-10 * -2 + t * -2) + t(-10 + t))(-18 + t) + 360 = 0
((20 + -2t) + t(-10 + t))(-18 + t) + 360 = 0
(20 + -2t + (-10 * t + t * t))(-18 + t) + 360 = 0
(20 + -2t + (-10t + t2))(-18 + t) + 360 = 0

Combine like terms: -2t + -10t = -12t
(20 + -12t + t2)(-18 + t) + 360 = 0

Multiply (20 + -12t + t2) * (-18 + t)
(20(-18 + t) + -12t * (-18 + t) + t2(-18 + t)) + 360 = 0
((-18 * 20 + t * 20) + -12t * (-18 + t) + t2(-18 + t)) + 360 = 0
((-360 + 20t) + -12t * (-18 + t) + t2(-18 + t)) + 360 = 0
(-360 + 20t + (-18 * -12t + t * -12t) + t2(-18 + t)) + 360 = 0
(-360 + 20t + (216t + -12t2) + t2(-18 + t)) + 360 = 0
(-360 + 20t + 216t + -12t2 + (-18 * t2 + t * t2)) + 360 = 0
(-360 + 20t + 216t + -12t2 + (-18t2 + t3)) + 360 = 0

Combine like terms: 20t + 216t = 236t
(-360 + 236t + -12t2 + -18t2 + t3) + 360 = 0

Combine like terms: -12t2 + -18t2 = -30t2
(-360 + 236t + -30t2 + t3) + 360 = 0

Reorder the terms:
-360 + 360 + 236t + -30t2 + t3 = 0

Combine like terms: -360 + 360 = 0
0 + 236t + -30t2 + t3 = 0
236t + -30t2 + t3 = 0

Solving
236t + -30t2 + t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(236 + -30t + t2) = 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 '(236 + -30t + t2)' equal to zero and attempt to solve:

Simplifying
236 + -30t + t2 = 0

Solving
236 + -30t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-236' to each side of the equation.
236 + -30t + -236 + t2 = 0 + -236

Reorder the terms:
236 + -236 + -30t + t2 = 0 + -236

Combine like terms: 236 + -236 = 0
0 + -30t + t2 = 0 + -236
-30t + t2 = 0 + -236

Combine like terms: 0 + -236 = -236
-30t + t2 = -236

The t term is -30t.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30t + 225 + t2 = -236 + 225

Reorder the terms:
225 + -30t + t2 = -236 + 225

Combine like terms: -236 + 225 = -11
225 + -30t + t2 = -11

Factor a perfect square on the left side:
(t + -15)(t + -15) = -11

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {0}

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