12=4(x-4)(x-7)

Solution for 12=4(x-4)(x-7) equation:

Simplifying
12 = 4(x + -4)(x + -7)

Reorder the terms:
12 = 4(-4 + x)(x + -7)

Reorder the terms:
12 = 4(-4 + x)(-7 + x)

Multiply (-4 + x) * (-7 + x)
12 = 4(-4(-7 + x) + x(-7 + x))
12 = 4((-7 * -4 + x * -4) + x(-7 + x))
12 = 4((28 + -4x) + x(-7 + x))
12 = 4(28 + -4x + (-7 * x + x * x))
12 = 4(28 + -4x + (-7x + x2))

Combine like terms: -4x + -7x = -11x
12 = 4(28 + -11x + x2)
12 = (28 * 4 + -11x * 4 + x2 * 4)
12 = (112 + -44x + 4x2)

Solving
12 = 112 + -44x + 4x2

Solving for variable 'x'.

Combine like terms: 12 + -112 = -100
-100 + 44x + -4x2 = 112 + -44x + 4x2 + -112 + 44x + -4x2

Reorder the terms:
-100 + 44x + -4x2 = 112 + -112 + -44x + 44x + 4x2 + -4x2

Combine like terms: 112 + -112 = 0
-100 + 44x + -4x2 = 0 + -44x + 44x + 4x2 + -4x2
-100 + 44x + -4x2 = -44x + 44x + 4x2 + -4x2

Combine like terms: -44x + 44x = 0
-100 + 44x + -4x2 = 0 + 4x2 + -4x2
-100 + 44x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-100 + 44x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + 11x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-25 + 11x + -1x2)' equal to zero and attempt to solve:

Simplifying
-25 + 11x + -1x2 = 0

Solving
-25 + 11x + -1x2 = 0

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

Divide each side by '-1'.
25 + -11x + x2 = 0

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -11x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + -11x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -11x + x2 = 0 + -25
-11x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
-11x + x2 = -25

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -25 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -25 + 30.25

Combine like terms: -25 + 30.25 = 5.25
30.25 + -11x + x2 = 5.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + -5.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
x + -5.5 = 2.291287847

Simplifying
x + -5.5 = 2.291287847

Reorder the terms:
-5.5 + x = 2.291287847

Solving
-5.5 + x = 2.291287847

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 2.291287847 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 2.291287847 + 5.5
x = 2.291287847 + 5.5

Combine like terms: 2.291287847 + 5.5 = 7.791287847
x = 7.791287847

Simplifying
x = 7.791287847

Subproblem 2
x + -5.5 = -2.291287847

Simplifying
x + -5.5 = -2.291287847

Reorder the terms:
-5.5 + x = -2.291287847

Solving
-5.5 + x = -2.291287847

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -2.291287847 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -2.291287847 + 5.5
x = -2.291287847 + 5.5

Combine like terms: -2.291287847 + 5.5 = 3.208712153
x = 3.208712153

Simplifying
x = 3.208712153

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.791287847, 3.208712153}
Solution
x = {7.791287847, 3.208712153}