(4x+9)(2x-2)=(19x+25)(9x+1)

Solution for (4x+9)(2x-2)=(19x+25)(9x+1) equation:

Simplifying
(4x + 9)(2x + -2) = (19x + 25)(9x + 1)

Reorder the terms:
(9 + 4x)(2x + -2) = (19x + 25)(9x + 1)

Reorder the terms:
(9 + 4x)(-2 + 2x) = (19x + 25)(9x + 1)

Multiply (9 + 4x) * (-2 + 2x)
(9(-2 + 2x) + 4x * (-2 + 2x)) = (19x + 25)(9x + 1)
((-2 * 9 + 2x * 9) + 4x * (-2 + 2x)) = (19x + 25)(9x + 1)
((-18 + 18x) + 4x * (-2 + 2x)) = (19x + 25)(9x + 1)
(-18 + 18x + (-2 * 4x + 2x * 4x)) = (19x + 25)(9x + 1)
(-18 + 18x + (-8x + 8x2)) = (19x + 25)(9x + 1)

Combine like terms: 18x + -8x = 10x
(-18 + 10x + 8x2) = (19x + 25)(9x + 1)

Reorder the terms:
-18 + 10x + 8x2 = (25 + 19x)(9x + 1)

Reorder the terms:
-18 + 10x + 8x2 = (25 + 19x)(1 + 9x)

Multiply (25 + 19x) * (1 + 9x)
-18 + 10x + 8x2 = (25(1 + 9x) + 19x * (1 + 9x))
-18 + 10x + 8x2 = ((1 * 25 + 9x * 25) + 19x * (1 + 9x))
-18 + 10x + 8x2 = ((25 + 225x) + 19x * (1 + 9x))
-18 + 10x + 8x2 = (25 + 225x + (1 * 19x + 9x * 19x))
-18 + 10x + 8x2 = (25 + 225x + (19x + 171x2))

Combine like terms: 225x + 19x = 244x
-18 + 10x + 8x2 = (25 + 244x + 171x2)

Solving
-18 + 10x + 8x2 = 25 + 244x + 171x2

Solving for variable 'x'.

Reorder the terms:
-18 + -25 + 10x + -244x + 8x2 + -171x2 = 25 + 244x + 171x2 + -25 + -244x + -171x2

Combine like terms: -18 + -25 = -43
-43 + 10x + -244x + 8x2 + -171x2 = 25 + 244x + 171x2 + -25 + -244x + -171x2

Combine like terms: 10x + -244x = -234x
-43 + -234x + 8x2 + -171x2 = 25 + 244x + 171x2 + -25 + -244x + -171x2

Combine like terms: 8x2 + -171x2 = -163x2
-43 + -234x + -163x2 = 25 + 244x + 171x2 + -25 + -244x + -171x2

Reorder the terms:
-43 + -234x + -163x2 = 25 + -25 + 244x + -244x + 171x2 + -171x2

Combine like terms: 25 + -25 = 0
-43 + -234x + -163x2 = 0 + 244x + -244x + 171x2 + -171x2
-43 + -234x + -163x2 = 244x + -244x + 171x2 + -171x2

Combine like terms: 244x + -244x = 0
-43 + -234x + -163x2 = 0 + 171x2 + -171x2
-43 + -234x + -163x2 = 171x2 + -171x2

Combine like terms: 171x2 + -171x2 = 0
-43 + -234x + -163x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(43 + 234x + 163x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(43 + 234x + 163x2)' equal to zero and attempt to solve:

Simplifying
43 + 234x + 163x2 = 0

Solving
43 + 234x + 163x2 = 0

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

Divide each side by '163'.
0.263803681 + 1.435582822x + x2 = 0

Move the constant term to the right:

Add '-0.263803681' to each side of the equation.
0.263803681 + 1.435582822x + -0.263803681 + x2 = 0 + -0.263803681

Reorder the terms:
0.263803681 + -0.263803681 + 1.435582822x + x2 = 0 + -0.263803681

Combine like terms: 0.263803681 + -0.263803681 = 0.000000000
0.000000000 + 1.435582822x + x2 = 0 + -0.263803681
1.435582822x + x2 = 0 + -0.263803681

Combine like terms: 0 + -0.263803681 = -0.263803681
1.435582822x + x2 = -0.263803681

The x term is 1.435582822x.  Take half its coefficient (0.717791411).
Square it (0.5152245097) and add it to both sides.

Add '0.5152245097' to each side of the equation.
1.435582822x + 0.5152245097 + x2 = -0.263803681 + 0.5152245097

Reorder the terms:
0.5152245097 + 1.435582822x + x2 = -0.263803681 + 0.5152245097

Combine like terms: -0.263803681 + 0.5152245097 = 0.2514208287
0.5152245097 + 1.435582822x + x2 = 0.2514208287

Factor a perfect square on the left side:
(x + 0.717791411)(x + 0.717791411) = 0.2514208287

Calculate the square root of the right side: 0.501418816

Break this problem into two subproblems by setting 
(x + 0.717791411) equal to 0.501418816 and -0.501418816.

Subproblem 1
x + 0.717791411 = 0.501418816

Simplifying
x + 0.717791411 = 0.501418816

Reorder the terms:
0.717791411 + x = 0.501418816

Solving
0.717791411 + x = 0.501418816

Solving for variable 'x'.

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

Add '-0.717791411' to each side of the equation.
0.717791411 + -0.717791411 + x = 0.501418816 + -0.717791411

Combine like terms: 0.717791411 + -0.717791411 = 0.000000000
0.000000000 + x = 0.501418816 + -0.717791411
x = 0.501418816 + -0.717791411

Combine like terms: 0.501418816 + -0.717791411 = -0.216372595
x = -0.216372595

Simplifying
x = -0.216372595

Subproblem 2
x + 0.717791411 = -0.501418816

Simplifying
x + 0.717791411 = -0.501418816

Reorder the terms:
0.717791411 + x = -0.501418816

Solving
0.717791411 + x = -0.501418816

Solving for variable 'x'.

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

Add '-0.717791411' to each side of the equation.
0.717791411 + -0.717791411 + x = -0.501418816 + -0.717791411

Combine like terms: 0.717791411 + -0.717791411 = 0.000000000
0.000000000 + x = -0.501418816 + -0.717791411
x = -0.501418816 + -0.717791411

Combine like terms: -0.501418816 + -0.717791411 = -1.219210227
x = -1.219210227

Simplifying
x = -1.219210227

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.216372595, -1.219210227}
Solution
x = {-0.216372595, -1.219210227}