20=(x-7)(x+4)

Solution for 20=(x-7)(x+4) equation:

Simplifying
20 = (x + -7)(x + 4)

Reorder the terms:
20 = (-7 + x)(x + 4)

Reorder the terms:
20 = (-7 + x)(4 + x)

Multiply (-7 + x) * (4 + x)
20 = (-7(4 + x) + x(4 + x))
20 = ((4 * -7 + x * -7) + x(4 + x))
20 = ((-28 + -7x) + x(4 + x))
20 = (-28 + -7x + (4 * x + x * x))
20 = (-28 + -7x + (4x + x2))

Combine like terms: -7x + 4x = -3x
20 = (-28 + -3x + x2)

Solving
20 = -28 + -3x + x2

Solving for variable 'x'.

Combine like terms: 20 + 28 = 48
48 + 3x + -1x2 = -28 + -3x + x2 + 28 + 3x + -1x2

Reorder the terms:
48 + 3x + -1x2 = -28 + 28 + -3x + 3x + x2 + -1x2

Combine like terms: -28 + 28 = 0
48 + 3x + -1x2 = 0 + -3x + 3x + x2 + -1x2
48 + 3x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
48 + 3x + -1x2 = 0 + x2 + -1x2
48 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
48 + 3x + -1x2 = 0

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

Divide each side by '-1'.
-48 + -3x + x2 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -3x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + -3x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -3x + x2 = 0 + 48
-3x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
-3x + x2 = 48

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 48 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 48 + 2.25

Combine like terms: 48 + 2.25 = 50.25
2.25 + -3x + x2 = 50.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(x + -1.5) equal to 7.088723439 and -7.088723439.

Subproblem 1
x + -1.5 = 7.088723439

Simplifying
x + -1.5 = 7.088723439

Reorder the terms:
-1.5 + x = 7.088723439

Solving
-1.5 + x = 7.088723439

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 7.088723439 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 7.088723439 + 1.5
x = 7.088723439 + 1.5

Combine like terms: 7.088723439 + 1.5 = 8.588723439
x = 8.588723439

Simplifying
x = 8.588723439

Subproblem 2
x + -1.5 = -7.088723439

Simplifying
x + -1.5 = -7.088723439

Reorder the terms:
-1.5 + x = -7.088723439

Solving
-1.5 + x = -7.088723439

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -7.088723439 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -7.088723439 + 1.5
x = -7.088723439 + 1.5

Combine like terms: -7.088723439 + 1.5 = -5.588723439
x = -5.588723439

Simplifying
x = -5.588723439

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.588723439, -5.588723439}