198=(x+2)(x)(3)

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Solution for 198=(x+2)(x)(3) equation: 


Simplifying
198 = (x + 2)(x)(3)

Reorder the terms:
198 = (2 + x)(x)(3)

Reorder the terms for easier multiplication:
198 = 3x(2 + x)
198 = (2 * 3x + x * 3x)
198 = (6x + 3x2)

Solving
198 = 6x + 3x2

Solving for variable 'x'.

Reorder the terms:
198 + -6x + -3x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
198 + -6x + -3x2 = 0 + 3x2 + -3x2
198 + -6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
198 + -6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(66 + -2x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(66 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
66 + -2x + -1x2 = 0

Solving
66 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-66 + 2x + x2 = 0

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 2x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + 2x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 2x + x2 = 0 + 66
2x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
2x + x2 = 66

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 66 + 1

Reorder the terms:
1 + 2x + x2 = 66 + 1

Combine like terms: 66 + 1 = 67
1 + 2x + x2 = 67

Factor a perfect square on the left side:
(x + 1)(x + 1) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(x + 1) equal to 8.185352772 and -8.185352772.


Subproblem 1
x + 1 = 8.185352772

Simplifying
x + 1 = 8.185352772

Reorder the terms:
1 + x = 8.185352772

Solving
1 + x = 8.185352772

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 8.185352772 + -1

Combine like terms: 1 + -1 = 0
0 + x = 8.185352772 + -1
x = 8.185352772 + -1

Combine like terms: 8.185352772 + -1 = 7.185352772
x = 7.185352772

Simplifying
x = 7.185352772


Subproblem 2
x + 1 = -8.185352772

Simplifying
x + 1 = -8.185352772

Reorder the terms:
1 + x = -8.185352772

Solving
1 + x = -8.185352772

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -8.185352772 + -1

Combine like terms: 1 + -1 = 0
0 + x = -8.185352772 + -1
x = -8.185352772 + -1

Combine like terms: -8.185352772 + -1 = -9.185352772
x = -9.185352772

Simplifying
x = -9.185352772


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.185352772, -9.185352772}
Solution
x = {7.185352772, -9.185352772}

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