(x-3)(x+4)=(4+6)2

Solution for (x-3)(x+4)=(4+6)2 equation:

Simplifying
(x + -3)(x + 4) = (4 + 6) * 2

Reorder the terms:
(-3 + x)(x + 4) = (4 + 6) * 2

Reorder the terms:
(-3 + x)(4 + x) = (4 + 6) * 2

Multiply (-3 + x) * (4 + x)
(-3(4 + x) + x(4 + x)) = (4 + 6) * 2
((4 * -3 + x * -3) + x(4 + x)) = (4 + 6) * 2
((-12 + -3x) + x(4 + x)) = (4 + 6) * 2
(-12 + -3x + (4 * x + x * x)) = (4 + 6) * 2
(-12 + -3x + (4x + x2)) = (4 + 6) * 2

Combine like terms: -3x + 4x = 1x
(-12 + 1x + x2) = (4 + 6) * 2

Combine like terms: 4 + 6 = 10
-12 + 1x + x2 = (10) * 2

Multiply 10 * 2
-12 + 1x + x2 = 20

Solving
-12 + 1x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
-12 + -20 + 1x + x2 = 20 + -20

Combine like terms: -12 + -20 = -32
-32 + 1x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-32 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 1x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 1x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 1x + x2 = 0 + 32
1x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
1x + x2 = 32

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 = 32 + 0.25

Reorder the terms:
0.25 + x + x2 = 32 + 0.25

Combine like terms: 32 + 0.25 = 32.25
0.25 + x + x2 = 32.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
x + 0.5 = 5.678908346

Simplifying
x + 0.5 = 5.678908346

Reorder the terms:
0.5 + x = 5.678908346

Solving
0.5 + x = 5.678908346

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 = 5.678908346 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.678908346 + -0.5
x = 5.678908346 + -0.5

Combine like terms: 5.678908346 + -0.5 = 5.178908346
x = 5.178908346

Simplifying
x = 5.178908346

Subproblem 2
x + 0.5 = -5.678908346

Simplifying
x + 0.5 = -5.678908346

Reorder the terms:
0.5 + x = -5.678908346

Solving
0.5 + x = -5.678908346

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 = -5.678908346 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.678908346 + -0.5
x = -5.678908346 + -0.5

Combine like terms: -5.678908346 + -0.5 = -6.178908346
x = -6.178908346

Simplifying
x = -6.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.178908346, -6.178908346}