(x+4)(x-9)=48x

Solution for (x+4)(x-9)=48x equation:

Simplifying
(x + 4)(x + -9) = 48x

Reorder the terms:
(4 + x)(x + -9) = 48x

Reorder the terms:
(4 + x)(-9 + x) = 48x

Multiply (4 + x) * (-9 + x)
(4(-9 + x) + x(-9 + x)) = 48x
((-9 * 4 + x * 4) + x(-9 + x)) = 48x
((-36 + 4x) + x(-9 + x)) = 48x
(-36 + 4x + (-9 * x + x * x)) = 48x
(-36 + 4x + (-9x + x2)) = 48x

Combine like terms: 4x + -9x = -5x
(-36 + -5x + x2) = 48x

Solving
-36 + -5x + x2 = 48x

Solving for variable 'x'.

Reorder the terms:
-36 + -5x + -48x + x2 = 48x + -48x

Combine like terms: -5x + -48x = -53x
-36 + -53x + x2 = 48x + -48x

Combine like terms: 48x + -48x = 0
-36 + -53x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -53x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -53x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -53x + x2 = 0 + 36
-53x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-53x + x2 = 36

The x term is -53x.  Take half its coefficient (-26.5).
Square it (702.25) and add it to both sides.

Add '702.25' to each side of the equation.
-53x + 702.25 + x2 = 36 + 702.25

Reorder the terms:
702.25 + -53x + x2 = 36 + 702.25

Combine like terms: 36 + 702.25 = 738.25
702.25 + -53x + x2 = 738.25

Factor a perfect square on the left side:
(x + -26.5)(x + -26.5) = 738.25

Calculate the square root of the right side: 27.170756338

Break this problem into two subproblems by setting 
(x + -26.5) equal to 27.170756338 and -27.170756338.

Subproblem 1
x + -26.5 = 27.170756338

Simplifying
x + -26.5 = 27.170756338

Reorder the terms:
-26.5 + x = 27.170756338

Solving
-26.5 + x = 27.170756338

Solving for variable 'x'.

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

Add '26.5' to each side of the equation.
-26.5 + 26.5 + x = 27.170756338 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = 27.170756338 + 26.5
x = 27.170756338 + 26.5

Combine like terms: 27.170756338 + 26.5 = 53.670756338
x = 53.670756338

Simplifying
x = 53.670756338

Subproblem 2
x + -26.5 = -27.170756338

Simplifying
x + -26.5 = -27.170756338

Reorder the terms:
-26.5 + x = -27.170756338

Solving
-26.5 + x = -27.170756338

Solving for variable 'x'.

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

Add '26.5' to each side of the equation.
-26.5 + 26.5 + x = -27.170756338 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = -27.170756338 + 26.5
x = -27.170756338 + 26.5

Combine like terms: -27.170756338 + 26.5 = -0.670756338
x = -0.670756338

Simplifying
x = -0.670756338

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {53.670756338, -0.670756338}