133=(7x+4)(3x+9)

Solution for 133=(7x+4)(3x+9) equation:

Simplifying
133 = (7x + 4)(3x + 9)

Reorder the terms:
133 = (4 + 7x)(3x + 9)

Reorder the terms:
133 = (4 + 7x)(9 + 3x)

Multiply (4 + 7x) * (9 + 3x)
133 = (4(9 + 3x) + 7x * (9 + 3x))
133 = ((9 * 4 + 3x * 4) + 7x * (9 + 3x))
133 = ((36 + 12x) + 7x * (9 + 3x))
133 = (36 + 12x + (9 * 7x + 3x * 7x))
133 = (36 + 12x + (63x + 21x2))

Combine like terms: 12x + 63x = 75x
133 = (36 + 75x + 21x2)

Solving
133 = 36 + 75x + 21x2

Solving for variable 'x'.

Combine like terms: 133 + -36 = 97
97 + -75x + -21x2 = 36 + 75x + 21x2 + -36 + -75x + -21x2

Reorder the terms:
97 + -75x + -21x2 = 36 + -36 + 75x + -75x + 21x2 + -21x2

Combine like terms: 36 + -36 = 0
97 + -75x + -21x2 = 0 + 75x + -75x + 21x2 + -21x2
97 + -75x + -21x2 = 75x + -75x + 21x2 + -21x2

Combine like terms: 75x + -75x = 0
97 + -75x + -21x2 = 0 + 21x2 + -21x2
97 + -75x + -21x2 = 21x2 + -21x2

Combine like terms: 21x2 + -21x2 = 0
97 + -75x + -21x2 = 0

Begin completing the square.  Divide all terms by
-21 the coefficient of the squared term: 

Divide each side by '-21'.
-4.619047619 + 3.571428571x + x2 = 0

Move the constant term to the right:

Add '4.619047619' to each side of the equation.
-4.619047619 + 3.571428571x + 4.619047619 + x2 = 0 + 4.619047619

Reorder the terms:
-4.619047619 + 4.619047619 + 3.571428571x + x2 = 0 + 4.619047619

Combine like terms: -4.619047619 + 4.619047619 = 0.000000000
0.000000000 + 3.571428571x + x2 = 0 + 4.619047619
3.571428571x + x2 = 0 + 4.619047619

Combine like terms: 0 + 4.619047619 = 4.619047619
3.571428571x + x2 = 4.619047619

The x term is 3.571428571x.  Take half its coefficient (1.785714286).
Square it (3.188775511) and add it to both sides.

Add '3.188775511' to each side of the equation.
3.571428571x + 3.188775511 + x2 = 4.619047619 + 3.188775511

Reorder the terms:
3.188775511 + 3.571428571x + x2 = 4.619047619 + 3.188775511

Combine like terms: 4.619047619 + 3.188775511 = 7.80782313
3.188775511 + 3.571428571x + x2 = 7.80782313

Factor a perfect square on the left side:
(x + 1.785714286)(x + 1.785714286) = 7.80782313

Calculate the square root of the right side: 2.794248223

Break this problem into two subproblems by setting 
(x + 1.785714286) equal to 2.794248223 and -2.794248223.

Subproblem 1
x + 1.785714286 = 2.794248223

Simplifying
x + 1.785714286 = 2.794248223

Reorder the terms:
1.785714286 + x = 2.794248223

Solving
1.785714286 + x = 2.794248223

Solving for variable 'x'.

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

Add '-1.785714286' to each side of the equation.
1.785714286 + -1.785714286 + x = 2.794248223 + -1.785714286

Combine like terms: 1.785714286 + -1.785714286 = 0.000000000
0.000000000 + x = 2.794248223 + -1.785714286
x = 2.794248223 + -1.785714286

Combine like terms: 2.794248223 + -1.785714286 = 1.008533937
x = 1.008533937

Simplifying
x = 1.008533937

Subproblem 2
x + 1.785714286 = -2.794248223

Simplifying
x + 1.785714286 = -2.794248223

Reorder the terms:
1.785714286 + x = -2.794248223

Solving
1.785714286 + x = -2.794248223

Solving for variable 'x'.

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

Add '-1.785714286' to each side of the equation.
1.785714286 + -1.785714286 + x = -2.794248223 + -1.785714286

Combine like terms: 1.785714286 + -1.785714286 = 0.000000000
0.000000000 + x = -2.794248223 + -1.785714286
x = -2.794248223 + -1.785714286

Combine like terms: -2.794248223 + -1.785714286 = -4.579962509
x = -4.579962509

Simplifying
x = -4.579962509

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.008533937, -4.579962509}