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

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

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

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

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

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

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

Solving
-12 + 1x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
-12 + -3 + 1x + x2 = 3 + -3

Combine like terms: -12 + -3 = -15
-15 + 1x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-15 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 1x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 1x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 1x + x2 = 0 + 15
1x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
1x + x2 = 15

The x term is 1x.  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.
x + 0.25 + x2 = 15 + 0.25

Reorder the terms:
0.25 + x + x2 = 15 + 0.25

Combine like terms: 15 + 0.25 = 15.25
0.25 + x + x2 = 15.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
x + 0.5 = 3.905124838

Simplifying
x + 0.5 = 3.905124838

Reorder the terms:
0.5 + x = 3.905124838

Solving
0.5 + x = 3.905124838

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 = 3.905124838 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.905124838 + -0.5
x = 3.905124838 + -0.5

Combine like terms: 3.905124838 + -0.5 = 3.405124838
x = 3.405124838

Simplifying
x = 3.405124838

Subproblem 2
x + 0.5 = -3.905124838

Simplifying
x + 0.5 = -3.905124838

Reorder the terms:
0.5 + x = -3.905124838

Solving
0.5 + x = -3.905124838

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 = -3.905124838 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.905124838 + -0.5
x = -3.905124838 + -0.5

Combine like terms: -3.905124838 + -0.5 = -4.405124838
x = -4.405124838

Simplifying
x = -4.405124838

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.405124838, -4.405124838}