4x(2x-9)=4

Solution for 4x(2x-9)=4 equation:

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

Reorder the terms:
4x(-9 + 2x) = 4
(-9 * 4x + 2x * 4x) = 4
(-36x + 8x2) = 4

Solving
-36x + 8x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + -36x + 8x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -36x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -9x + 2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -9x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + -9x + 2x2 = 0

Solving
-1 + -9x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + -4.5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -4.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -4.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -4.5x + x2 = 0 + 0.5
-4.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-4.5x + x2 = 0.5

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 0.5 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 0.5 + 5.0625

Combine like terms: 0.5 + 5.0625 = 5.5625
5.0625 + -4.5x + x2 = 5.5625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.358495283 and -2.358495283.

Subproblem 1
x + -2.25 = 2.358495283

Simplifying
x + -2.25 = 2.358495283

Reorder the terms:
-2.25 + x = 2.358495283

Solving
-2.25 + x = 2.358495283

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.358495283 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.358495283 + 2.25
x = 2.358495283 + 2.25

Combine like terms: 2.358495283 + 2.25 = 4.608495283
x = 4.608495283

Simplifying
x = 4.608495283

Subproblem 2
x + -2.25 = -2.358495283

Simplifying
x + -2.25 = -2.358495283

Reorder the terms:
-2.25 + x = -2.358495283

Solving
-2.25 + x = -2.358495283

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.358495283 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.358495283 + 2.25
x = -2.358495283 + 2.25

Combine like terms: -2.358495283 + 2.25 = -0.108495283
x = -0.108495283

Simplifying
x = -0.108495283

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.608495283, -0.108495283}
Solution
x = {4.608495283, -0.108495283}