(5x+4)(x-20)=62-(x+2)

Solution for (5x+4)(x-20)=62-(x+2) equation:

Simplifying
(5x + 4)(x + -20) = 62 + -1(x + 2)

Reorder the terms:
(4 + 5x)(x + -20) = 62 + -1(x + 2)

Reorder the terms:
(4 + 5x)(-20 + x) = 62 + -1(x + 2)

Multiply (4 + 5x) * (-20 + x)
(4(-20 + x) + 5x * (-20 + x)) = 62 + -1(x + 2)
((-20 * 4 + x * 4) + 5x * (-20 + x)) = 62 + -1(x + 2)
((-80 + 4x) + 5x * (-20 + x)) = 62 + -1(x + 2)
(-80 + 4x + (-20 * 5x + x * 5x)) = 62 + -1(x + 2)
(-80 + 4x + (-100x + 5x2)) = 62 + -1(x + 2)

Combine like terms: 4x + -100x = -96x
(-80 + -96x + 5x2) = 62 + -1(x + 2)

Reorder the terms:
-80 + -96x + 5x2 = 62 + -1(2 + x)
-80 + -96x + 5x2 = 62 + (2 * -1 + x * -1)
-80 + -96x + 5x2 = 62 + (-2 + -1x)

Combine like terms: 62 + -2 = 60
-80 + -96x + 5x2 = 60 + -1x

Solving
-80 + -96x + 5x2 = 60 + -1x

Solving for variable 'x'.

Reorder the terms:
-80 + -60 + -96x + x + 5x2 = 60 + -1x + -60 + x

Combine like terms: -80 + -60 = -140
-140 + -96x + x + 5x2 = 60 + -1x + -60 + x

Combine like terms: -96x + x = -95x
-140 + -95x + 5x2 = 60 + -1x + -60 + x

Reorder the terms:
-140 + -95x + 5x2 = 60 + -60 + -1x + x

Combine like terms: 60 + -60 = 0
-140 + -95x + 5x2 = 0 + -1x + x
-140 + -95x + 5x2 = -1x + x

Combine like terms: -1x + x = 0
-140 + -95x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-28 + -19x + x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-28 + -19x + x2)' equal to zero and attempt to solve:

Simplifying
-28 + -19x + x2 = 0

Solving
-28 + -19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -19x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -19x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -19x + x2 = 0 + 28
-19x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-19x + x2 = 28

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = 28 + 90.25

Reorder the terms:
90.25 + -19x + x2 = 28 + 90.25

Combine like terms: 28 + 90.25 = 118.25
90.25 + -19x + x2 = 118.25

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 118.25

Calculate the square root of the right side: 10.874281585

Break this problem into two subproblems by setting 
(x + -9.5) equal to 10.874281585 and -10.874281585.

Subproblem 1
x + -9.5 = 10.874281585

Simplifying
x + -9.5 = 10.874281585

Reorder the terms:
-9.5 + x = 10.874281585

Solving
-9.5 + x = 10.874281585

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = 10.874281585 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 10.874281585 + 9.5
x = 10.874281585 + 9.5

Combine like terms: 10.874281585 + 9.5 = 20.374281585
x = 20.374281585

Simplifying
x = 20.374281585

Subproblem 2
x + -9.5 = -10.874281585

Simplifying
x + -9.5 = -10.874281585

Reorder the terms:
-9.5 + x = -10.874281585

Solving
-9.5 + x = -10.874281585

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = -10.874281585 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -10.874281585 + 9.5
x = -10.874281585 + 9.5

Combine like terms: -10.874281585 + 9.5 = -1.374281585
x = -1.374281585

Simplifying
x = -1.374281585

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.374281585, -1.374281585}
Solution
x = {20.374281585, -1.374281585}