(7x+2)(x-20)=62-(x+2)

Solution for (7x+2)(x-20)=62-(x+2) equation:

Simplifying
(7x + 2)(x + -20) = 62 + -1(x + 2)

Reorder the terms:
(2 + 7x)(x + -20) = 62 + -1(x + 2)

Reorder the terms:
(2 + 7x)(-20 + x) = 62 + -1(x + 2)

Multiply (2 + 7x) * (-20 + x)
(2(-20 + x) + 7x * (-20 + x)) = 62 + -1(x + 2)
((-20 * 2 + x * 2) + 7x * (-20 + x)) = 62 + -1(x + 2)
((-40 + 2x) + 7x * (-20 + x)) = 62 + -1(x + 2)
(-40 + 2x + (-20 * 7x + x * 7x)) = 62 + -1(x + 2)
(-40 + 2x + (-140x + 7x2)) = 62 + -1(x + 2)

Combine like terms: 2x + -140x = -138x
(-40 + -138x + 7x2) = 62 + -1(x + 2)

Reorder the terms:
-40 + -138x + 7x2 = 62 + -1(2 + x)
-40 + -138x + 7x2 = 62 + (2 * -1 + x * -1)
-40 + -138x + 7x2 = 62 + (-2 + -1x)

Combine like terms: 62 + -2 = 60
-40 + -138x + 7x2 = 60 + -1x

Solving
-40 + -138x + 7x2 = 60 + -1x

Solving for variable 'x'.

Reorder the terms:
-40 + -60 + -138x + x + 7x2 = 60 + -1x + -60 + x

Combine like terms: -40 + -60 = -100
-100 + -138x + x + 7x2 = 60 + -1x + -60 + x

Combine like terms: -138x + x = -137x
-100 + -137x + 7x2 = 60 + -1x + -60 + x

Reorder the terms:
-100 + -137x + 7x2 = 60 + -60 + -1x + x

Combine like terms: 60 + -60 = 0
-100 + -137x + 7x2 = 0 + -1x + x
-100 + -137x + 7x2 = -1x + x

Combine like terms: -1x + x = 0
-100 + -137x + 7x2 = 0

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

Divide each side by '7'.
-14.28571429 + -19.57142857x + x2 = 0

Move the constant term to the right:

Add '14.28571429' to each side of the equation.
-14.28571429 + -19.57142857x + 14.28571429 + x2 = 0 + 14.28571429

Reorder the terms:
-14.28571429 + 14.28571429 + -19.57142857x + x2 = 0 + 14.28571429

Combine like terms: -14.28571429 + 14.28571429 = 0.00000000
0.00000000 + -19.57142857x + x2 = 0 + 14.28571429
-19.57142857x + x2 = 0 + 14.28571429

Combine like terms: 0 + 14.28571429 = 14.28571429
-19.57142857x + x2 = 14.28571429

The x term is -19.57142857x.  Take half its coefficient (-9.785714285).
Square it (95.76020407) and add it to both sides.

Add '95.76020407' to each side of the equation.
-19.57142857x + 95.76020407 + x2 = 14.28571429 + 95.76020407

Reorder the terms:
95.76020407 + -19.57142857x + x2 = 14.28571429 + 95.76020407

Combine like terms: 14.28571429 + 95.76020407 = 110.04591836
95.76020407 + -19.57142857x + x2 = 110.04591836

Factor a perfect square on the left side:
(x + -9.785714285)(x + -9.785714285) = 110.04591836

Calculate the square root of the right side: 10.490277325

Break this problem into two subproblems by setting 
(x + -9.785714285) equal to 10.490277325 and -10.490277325.

Subproblem 1
x + -9.785714285 = 10.490277325

Simplifying
x + -9.785714285 = 10.490277325

Reorder the terms:
-9.785714285 + x = 10.490277325

Solving
-9.785714285 + x = 10.490277325

Solving for variable 'x'.

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

Add '9.785714285' to each side of the equation.
-9.785714285 + 9.785714285 + x = 10.490277325 + 9.785714285

Combine like terms: -9.785714285 + 9.785714285 = 0.000000000
0.000000000 + x = 10.490277325 + 9.785714285
x = 10.490277325 + 9.785714285

Combine like terms: 10.490277325 + 9.785714285 = 20.27599161
x = 20.27599161

Simplifying
x = 20.27599161

Subproblem 2
x + -9.785714285 = -10.490277325

Simplifying
x + -9.785714285 = -10.490277325

Reorder the terms:
-9.785714285 + x = -10.490277325

Solving
-9.785714285 + x = -10.490277325

Solving for variable 'x'.

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

Add '9.785714285' to each side of the equation.
-9.785714285 + 9.785714285 + x = -10.490277325 + 9.785714285

Combine like terms: -9.785714285 + 9.785714285 = 0.000000000
0.000000000 + x = -10.490277325 + 9.785714285
x = -10.490277325 + 9.785714285

Combine like terms: -10.490277325 + 9.785714285 = -0.70456304
x = -0.70456304

Simplifying
x = -0.70456304

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.27599161, -0.70456304}