(6x+3)(x-20)=62-(x+2)

Solution for (6x+3)(x-20)=62-(x+2) equation:

Simplifying
(6x + 3)(x + -20) = 62 + -1(x + 2)

Reorder the terms:
(3 + 6x)(x + -20) = 62 + -1(x + 2)

Reorder the terms:
(3 + 6x)(-20 + x) = 62 + -1(x + 2)

Multiply (3 + 6x) * (-20 + x)
(3(-20 + x) + 6x * (-20 + x)) = 62 + -1(x + 2)
((-20 * 3 + x * 3) + 6x * (-20 + x)) = 62 + -1(x + 2)
((-60 + 3x) + 6x * (-20 + x)) = 62 + -1(x + 2)
(-60 + 3x + (-20 * 6x + x * 6x)) = 62 + -1(x + 2)
(-60 + 3x + (-120x + 6x2)) = 62 + -1(x + 2)

Combine like terms: 3x + -120x = -117x
(-60 + -117x + 6x2) = 62 + -1(x + 2)

Reorder the terms:
-60 + -117x + 6x2 = 62 + -1(2 + x)
-60 + -117x + 6x2 = 62 + (2 * -1 + x * -1)
-60 + -117x + 6x2 = 62 + (-2 + -1x)

Combine like terms: 62 + -2 = 60
-60 + -117x + 6x2 = 60 + -1x

Solving
-60 + -117x + 6x2 = 60 + -1x

Solving for variable 'x'.

Reorder the terms:
-60 + -60 + -117x + x + 6x2 = 60 + -1x + -60 + x

Combine like terms: -60 + -60 = -120
-120 + -117x + x + 6x2 = 60 + -1x + -60 + x

Combine like terms: -117x + x = -116x
-120 + -116x + 6x2 = 60 + -1x + -60 + x

Reorder the terms:
-120 + -116x + 6x2 = 60 + -60 + -1x + x

Combine like terms: 60 + -60 = 0
-120 + -116x + 6x2 = 0 + -1x + x
-120 + -116x + 6x2 = -1x + x

Combine like terms: -1x + x = 0
-120 + -116x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + -58x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-60 + -58x + 3x2)' equal to zero and attempt to solve:

Simplifying
-60 + -58x + 3x2 = 0

Solving
-60 + -58x + 3x2 = 0

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

Divide each side by '3'.
-20 + -19.33333333x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -19.33333333x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -19.33333333x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -19.33333333x + x2 = 0 + 20
-19.33333333x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-19.33333333x + x2 = 20

The x term is -19.33333333x.  Take half its coefficient (-9.666666665).
Square it (93.44444441) and add it to both sides.

Add '93.44444441' to each side of the equation.
-19.33333333x + 93.44444441 + x2 = 20 + 93.44444441

Reorder the terms:
93.44444441 + -19.33333333x + x2 = 20 + 93.44444441

Combine like terms: 20 + 93.44444441 = 113.44444441
93.44444441 + -19.33333333x + x2 = 113.44444441

Factor a perfect square on the left side:
(x + -9.666666665)(x + -9.666666665) = 113.44444441

Calculate the square root of the right side: 10.651030204

Break this problem into two subproblems by setting 
(x + -9.666666665) equal to 10.651030204 and -10.651030204.

Subproblem 1
x + -9.666666665 = 10.651030204

Simplifying
x + -9.666666665 = 10.651030204

Reorder the terms:
-9.666666665 + x = 10.651030204

Solving
-9.666666665 + x = 10.651030204

Solving for variable 'x'.

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

Add '9.666666665' to each side of the equation.
-9.666666665 + 9.666666665 + x = 10.651030204 + 9.666666665

Combine like terms: -9.666666665 + 9.666666665 = 0.000000000
0.000000000 + x = 10.651030204 + 9.666666665
x = 10.651030204 + 9.666666665

Combine like terms: 10.651030204 + 9.666666665 = 20.317696869
x = 20.317696869

Simplifying
x = 20.317696869

Subproblem 2
x + -9.666666665 = -10.651030204

Simplifying
x + -9.666666665 = -10.651030204

Reorder the terms:
-9.666666665 + x = -10.651030204

Solving
-9.666666665 + x = -10.651030204

Solving for variable 'x'.

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

Add '9.666666665' to each side of the equation.
-9.666666665 + 9.666666665 + x = -10.651030204 + 9.666666665

Combine like terms: -9.666666665 + 9.666666665 = 0.000000000
0.000000000 + x = -10.651030204 + 9.666666665
x = -10.651030204 + 9.666666665

Combine like terms: -10.651030204 + 9.666666665 = -0.984363539
x = -0.984363539

Simplifying
x = -0.984363539

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.317696869, -0.984363539}
Solution
x = {20.317696869, -0.984363539}