48=(x-4)(x+3)

Solution for 48=(x-4)(x+3) equation:

Simplifying
48 = (x + -4)(x + 3)

Reorder the terms:
48 = (-4 + x)(x + 3)

Reorder the terms:
48 = (-4 + x)(3 + x)

Multiply (-4 + x) * (3 + x)
48 = (-4(3 + x) + x(3 + x))
48 = ((3 * -4 + x * -4) + x(3 + x))
48 = ((-12 + -4x) + x(3 + x))
48 = (-12 + -4x + (3 * x + x * x))
48 = (-12 + -4x + (3x + x2))

Combine like terms: -4x + 3x = -1x
48 = (-12 + -1x + x2)

Solving
48 = -12 + -1x + x2

Solving for variable 'x'.

Combine like terms: 48 + 12 = 60
60 + x + -1x2 = -12 + -1x + x2 + 12 + x + -1x2

Reorder the terms:
60 + x + -1x2 = -12 + 12 + -1x + x + x2 + -1x2

Combine like terms: -12 + 12 = 0
60 + x + -1x2 = 0 + -1x + x + x2 + -1x2
60 + x + -1x2 = -1x + x + x2 + -1x2

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

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

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

Divide each side by '-1'.
-60 + -1x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -1x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -1x + x2 = 0 + 60

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 60 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 60 + 0.25

Combine like terms: 60 + 0.25 = 60.25
0.25 + -1x + x2 = 60.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(x + 0.5) equal to 7.762087348 and -7.762087348.

Subproblem 1
x + 0.5 = 7.762087348

Simplifying
x + 0.5 = 7.762087348

Reorder the terms:
0.5 + x = 7.762087348

Solving
0.5 + x = 7.762087348

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 7.762087348 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 7.762087348 + -0.5
x = 7.762087348 + -0.5

Combine like terms: 7.762087348 + -0.5 = 7.262087348
x = 7.262087348

Simplifying
x = 7.262087348

Subproblem 2
x + 0.5 = -7.762087348

Simplifying
x + 0.5 = -7.762087348

Reorder the terms:
0.5 + x = -7.762087348

Solving
0.5 + x = -7.762087348

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -7.762087348 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -7.762087348 + -0.5
x = -7.762087348 + -0.5

Combine like terms: -7.762087348 + -0.5 = -8.262087348
x = -8.262087348

Simplifying
x = -8.262087348

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.262087348, -8.262087348}