(4x+1)*(2x)=9

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Solution for (4x+1)*(2x)=9 equation: 


Simplifying
(4x + 1)(2x) = 9

Reorder the terms:
(1 + 4x)(2x) = 9

Remove parenthesis around (2x)
(1 + 4x) * 2x = 9

Reorder the terms for easier multiplication:
2x(1 + 4x) = 9
(1 * 2x + 4x * 2x) = 9
(2x + 8x2) = 9

Solving
2x + 8x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 2x + 8x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 2x + 8x2 = 0

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

Divide each side by '8'.
-1.125 + 0.25x + x2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + 0.25x + 1.125 + x2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + 0.25x + x2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + 0.25x + x2 = 0 + 1.125
0.25x + x2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
0.25x + x2 = 1.125

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 1.125 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 1.125 + 0.015625

Combine like terms: 1.125 + 0.015625 = 1.140625
0.015625 + 0.25x + x2 = 1.140625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x + 0.125) equal to 1.068000468 and -1.068000468.


Subproblem 1
x + 0.125 = 1.068000468

Simplifying
x + 0.125 = 1.068000468

Reorder the terms:
0.125 + x = 1.068000468

Solving
0.125 + x = 1.068000468

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 1.068000468 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 1.068000468 + -0.125
x = 1.068000468 + -0.125

Combine like terms: 1.068000468 + -0.125 = 0.943000468
x = 0.943000468

Simplifying
x = 0.943000468


Subproblem 2
x + 0.125 = -1.068000468

Simplifying
x + 0.125 = -1.068000468

Reorder the terms:
0.125 + x = -1.068000468

Solving
0.125 + x = -1.068000468

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -1.068000468 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -1.068000468 + -0.125
x = -1.068000468 + -0.125

Combine like terms: -1.068000468 + -0.125 = -1.193000468
x = -1.193000468

Simplifying
x = -1.193000468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.943000468, -1.193000468}

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