4(x+3)(x+4)=64

Solution for 4(x+3)(x+4)=64 equation:

Simplifying
4(x + 3)(x + 4) = 64

Reorder the terms:
4(3 + x)(x + 4) = 64

Reorder the terms:
4(3 + x)(4 + x) = 64

Multiply (3 + x) * (4 + x)
4(3(4 + x) + x(4 + x)) = 64
4((4 * 3 + x * 3) + x(4 + x)) = 64
4((12 + 3x) + x(4 + x)) = 64
4(12 + 3x + (4 * x + x * x)) = 64
4(12 + 3x + (4x + x2)) = 64

Combine like terms: 3x + 4x = 7x
4(12 + 7x + x2) = 64
(12 * 4 + 7x * 4 + x2 * 4) = 64
(48 + 28x + 4x2) = 64

Solving
48 + 28x + 4x2 = 64

Solving for variable 'x'.

Reorder the terms:
48 + -64 + 28x + 4x2 = 64 + -64

Combine like terms: 48 + -64 = -16
-16 + 28x + 4x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-16 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 7x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + 7x + x2 = 0

Solving
-4 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 7x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 7x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 7x + x2 = 0 + 4
7x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
7x + x2 = 4

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 4 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 4 + 12.25

Combine like terms: 4 + 12.25 = 16.25
12.25 + 7x + x2 = 16.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
x + 3.5 = 4.031128874

Simplifying
x + 3.5 = 4.031128874

Reorder the terms:
3.5 + x = 4.031128874

Solving
3.5 + x = 4.031128874

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 4.031128874 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.031128874 + -3.5
x = 4.031128874 + -3.5

Combine like terms: 4.031128874 + -3.5 = 0.531128874
x = 0.531128874

Simplifying
x = 0.531128874

Subproblem 2
x + 3.5 = -4.031128874

Simplifying
x + 3.5 = -4.031128874

Reorder the terms:
3.5 + x = -4.031128874

Solving
3.5 + x = -4.031128874

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -4.031128874 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.031128874 + -3.5
x = -4.031128874 + -3.5

Combine like terms: -4.031128874 + -3.5 = -7.531128874
x = -7.531128874

Simplifying
x = -7.531128874

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.531128874, -7.531128874}
Solution
x = {0.531128874, -7.531128874}