(4x+2)(4x+9)=(4x+6)

Solution for (4x+2)(4x+9)=(4x+6) equation:

Simplifying
(4x + 2)(4x + 9) = (4x + 6)

Reorder the terms:
(2 + 4x)(4x + 9) = (4x + 6)

Reorder the terms:
(2 + 4x)(9 + 4x) = (4x + 6)

Multiply (2 + 4x) * (9 + 4x)
(2(9 + 4x) + 4x * (9 + 4x)) = (4x + 6)
((9 * 2 + 4x * 2) + 4x * (9 + 4x)) = (4x + 6)
((18 + 8x) + 4x * (9 + 4x)) = (4x + 6)
(18 + 8x + (9 * 4x + 4x * 4x)) = (4x + 6)
(18 + 8x + (36x + 16x2)) = (4x + 6)

Combine like terms: 8x + 36x = 44x
(18 + 44x + 16x2) = (4x + 6)

Reorder the terms:
18 + 44x + 16x2 = (6 + 4x)

Remove parenthesis around (6 + 4x)
18 + 44x + 16x2 = 6 + 4x

Solving
18 + 44x + 16x2 = 6 + 4x

Solving for variable 'x'.

Reorder the terms:
18 + -6 + 44x + -4x + 16x2 = 6 + 4x + -6 + -4x

Combine like terms: 18 + -6 = 12
12 + 44x + -4x + 16x2 = 6 + 4x + -6 + -4x

Combine like terms: 44x + -4x = 40x
12 + 40x + 16x2 = 6 + 4x + -6 + -4x

Reorder the terms:
12 + 40x + 16x2 = 6 + -6 + 4x + -4x

Combine like terms: 6 + -6 = 0
12 + 40x + 16x2 = 0 + 4x + -4x
12 + 40x + 16x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
12 + 40x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 10x + 4x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + 10x + 4x2)' equal to zero and attempt to solve:

Simplifying
3 + 10x + 4x2 = 0

Solving
3 + 10x + 4x2 = 0

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

Divide each side by '4'.
0.75 + 2.5x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 2.5x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 2.5x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 2.5x + x2 = 0 + -0.75
2.5x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
2.5x + x2 = -0.75

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -0.75 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -0.75 + 1.5625

Combine like terms: -0.75 + 1.5625 = 0.8125
1.5625 + 2.5x + x2 = 0.8125

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(x + 1.25) equal to 0.901387819 and -0.901387819.

Subproblem 1
x + 1.25 = 0.901387819

Simplifying
x + 1.25 = 0.901387819

Reorder the terms:
1.25 + x = 0.901387819

Solving
1.25 + x = 0.901387819

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 0.901387819 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 0.901387819 + -1.25
x = 0.901387819 + -1.25

Combine like terms: 0.901387819 + -1.25 = -0.348612181
x = -0.348612181

Simplifying
x = -0.348612181

Subproblem 2
x + 1.25 = -0.901387819

Simplifying
x + 1.25 = -0.901387819

Reorder the terms:
1.25 + x = -0.901387819

Solving
1.25 + x = -0.901387819

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -0.901387819 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -0.901387819 + -1.25
x = -0.901387819 + -1.25

Combine like terms: -0.901387819 + -1.25 = -2.151387819
x = -2.151387819

Simplifying
x = -2.151387819

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.348612181, -2.151387819}
Solution
x = {-0.348612181, -2.151387819}