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

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


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

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

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

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

Multiply (-2 + x) * (-10 + x)
(-2(-10 + x) + x(-10 + x))(-18 + x) + 360 = 0
((-10 * -2 + x * -2) + x(-10 + x))(-18 + x) + 360 = 0
((20 + -2x) + x(-10 + x))(-18 + x) + 360 = 0
(20 + -2x + (-10 * x + x * x))(-18 + x) + 360 = 0
(20 + -2x + (-10x + x2))(-18 + x) + 360 = 0

Combine like terms: -2x + -10x = -12x
(20 + -12x + x2)(-18 + x) + 360 = 0

Multiply (20 + -12x + x2) * (-18 + x)
(20(-18 + x) + -12x * (-18 + x) + x2(-18 + x)) + 360 = 0
((-18 * 20 + x * 20) + -12x * (-18 + x) + x2(-18 + x)) + 360 = 0
((-360 + 20x) + -12x * (-18 + x) + x2(-18 + x)) + 360 = 0
(-360 + 20x + (-18 * -12x + x * -12x) + x2(-18 + x)) + 360 = 0
(-360 + 20x + (216x + -12x2) + x2(-18 + x)) + 360 = 0
(-360 + 20x + 216x + -12x2 + (-18 * x2 + x * x2)) + 360 = 0
(-360 + 20x + 216x + -12x2 + (-18x2 + x3)) + 360 = 0

Combine like terms: 20x + 216x = 236x
(-360 + 236x + -12x2 + -18x2 + x3) + 360 = 0

Combine like terms: -12x2 + -18x2 = -30x2
(-360 + 236x + -30x2 + x3) + 360 = 0

Reorder the terms:
-360 + 360 + 236x + -30x2 + x3 = 0

Combine like terms: -360 + 360 = 0
0 + 236x + -30x2 + x3 = 0
236x + -30x2 + x3 = 0

Solving
236x + -30x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(236 + -30x + x2) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(236 + -30x + x2)' equal to zero and attempt to solve:

Simplifying
236 + -30x + x2 = 0

Solving
236 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-236' to each side of the equation.
236 + -30x + -236 + x2 = 0 + -236

Reorder the terms:
236 + -236 + -30x + x2 = 0 + -236

Combine like terms: 236 + -236 = 0
0 + -30x + x2 = 0 + -236
-30x + x2 = 0 + -236

Combine like terms: 0 + -236 = -236
-30x + x2 = -236

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

Add '225' to each side of the equation.
-30x + 225 + x2 = -236 + 225

Reorder the terms:
225 + -30x + x2 = -236 + 225

Combine like terms: -236 + 225 = -11
225 + -30x + x2 = -11

Factor a perfect square on the left side:
(x + -15)(x + -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
x = {0}

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