198=2(x+7)(x-3)

Solution for 198=2(x+7)(x-3) equation:

Simplifying
198 = 2(x + 7)(x + -3)

Reorder the terms:
198 = 2(7 + x)(x + -3)

Reorder the terms:
198 = 2(7 + x)(-3 + x)

Multiply (7 + x) * (-3 + x)
198 = 2(7(-3 + x) + x(-3 + x))
198 = 2((-3 * 7 + x * 7) + x(-3 + x))
198 = 2((-21 + 7x) + x(-3 + x))
198 = 2(-21 + 7x + (-3 * x + x * x))
198 = 2(-21 + 7x + (-3x + x2))

Combine like terms: 7x + -3x = 4x
198 = 2(-21 + 4x + x2)
198 = (-21 * 2 + 4x * 2 + x2 * 2)
198 = (-42 + 8x + 2x2)

Solving
198 = -42 + 8x + 2x2

Solving for variable 'x'.

Combine like terms: 198 + 42 = 240
240 + -8x + -2x2 = -42 + 8x + 2x2 + 42 + -8x + -2x2

Reorder the terms:
240 + -8x + -2x2 = -42 + 42 + 8x + -8x + 2x2 + -2x2

Combine like terms: -42 + 42 = 0
240 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
240 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
240 + -8x + -2x2 = 0 + 2x2 + -2x2
240 + -8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
240 + -8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(120 + -4x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(120 + -4x + -1x2)' equal to zero and attempt to solve:

Simplifying
120 + -4x + -1x2 = 0

Solving
120 + -4x + -1x2 = 0

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

Divide each side by '-1'.
-120 + 4x + x2 = 0

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 4x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + 4x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 4x + x2 = 0 + 120
4x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
4x + x2 = 120

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 120 + 4

Reorder the terms:
4 + 4x + x2 = 120 + 4

Combine like terms: 120 + 4 = 124
4 + 4x + x2 = 124

Factor a perfect square on the left side:
(x + 2)(x + 2) = 124

Calculate the square root of the right side: 11.135528726

Break this problem into two subproblems by setting 
(x + 2) equal to 11.135528726 and -11.135528726.

Subproblem 1
x + 2 = 11.135528726

Simplifying
x + 2 = 11.135528726

Reorder the terms:
2 + x = 11.135528726

Solving
2 + x = 11.135528726

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 11.135528726 + -2

Combine like terms: 2 + -2 = 0
0 + x = 11.135528726 + -2
x = 11.135528726 + -2

Combine like terms: 11.135528726 + -2 = 9.135528726
x = 9.135528726

Simplifying
x = 9.135528726

Subproblem 2
x + 2 = -11.135528726

Simplifying
x + 2 = -11.135528726

Reorder the terms:
2 + x = -11.135528726

Solving
2 + x = -11.135528726

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -11.135528726 + -2

Combine like terms: 2 + -2 = 0
0 + x = -11.135528726 + -2
x = -11.135528726 + -2

Combine like terms: -11.135528726 + -2 = -13.135528726
x = -13.135528726

Simplifying
x = -13.135528726

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.135528726, -13.135528726}
Solution
x = {9.135528726, -13.135528726}