8x-2(5x-4)(9x-3)=

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Solution for 8x-2(5x-4)(9x-3)= equation: 


Simplifying
8x + -2(5x + -4)(9x + -3) = 0

Reorder the terms:
8x + -2(-4 + 5x)(9x + -3) = 0

Reorder the terms:
8x + -2(-4 + 5x)(-3 + 9x) = 0

Multiply (-4 + 5x) * (-3 + 9x)
8x + -2(-4(-3 + 9x) + 5x * (-3 + 9x)) = 0
8x + -2((-3 * -4 + 9x * -4) + 5x * (-3 + 9x)) = 0
8x + -2((12 + -36x) + 5x * (-3 + 9x)) = 0
8x + -2(12 + -36x + (-3 * 5x + 9x * 5x)) = 0
8x + -2(12 + -36x + (-15x + 45x2)) = 0

Combine like terms: -36x + -15x = -51x
8x + -2(12 + -51x + 45x2) = 0
8x + (12 * -2 + -51x * -2 + 45x2 * -2) = 0
8x + (-24 + 102x + -90x2) = 0

Reorder the terms:
-24 + 8x + 102x + -90x2 = 0

Combine like terms: 8x + 102x = 110x
-24 + 110x + -90x2 = 0

Solving
-24 + 110x + -90x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 55x + -45x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 55x + -45x2)' equal to zero and attempt to solve:

Simplifying
-12 + 55x + -45x2 = 0

Solving
-12 + 55x + -45x2 = 0

Begin completing the square.  Divide all terms by
-45 the coefficient of the squared term: 

Divide each side by '-45'.
0.2666666667 + -1.222222222x + x2 = 0

Move the constant term to the right:

Add '-0.2666666667' to each side of the equation.
0.2666666667 + -1.222222222x + -0.2666666667 + x2 = 0 + -0.2666666667

Reorder the terms:
0.2666666667 + -0.2666666667 + -1.222222222x + x2 = 0 + -0.2666666667

Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000
0.0000000000 + -1.222222222x + x2 = 0 + -0.2666666667
-1.222222222x + x2 = 0 + -0.2666666667

Combine like terms: 0 + -0.2666666667 = -0.2666666667
-1.222222222x + x2 = -0.2666666667

The x term is -1.222222222x.  Take half its coefficient (-0.611111111).
Square it (0.3734567900) and add it to both sides.

Add '0.3734567900' to each side of the equation.
-1.222222222x + 0.3734567900 + x2 = -0.2666666667 + 0.3734567900

Reorder the terms:
0.3734567900 + -1.222222222x + x2 = -0.2666666667 + 0.3734567900

Combine like terms: -0.2666666667 + 0.3734567900 = 0.1067901233
0.3734567900 + -1.222222222x + x2 = 0.1067901233

Factor a perfect square on the left side:
(x + -0.611111111)(x + -0.611111111) = 0.1067901233

Calculate the square root of the right side: 0.326787581

Break this problem into two subproblems by setting 
(x + -0.611111111) equal to 0.326787581 and -0.326787581.


Subproblem 1
x + -0.611111111 = 0.326787581

Simplifying
x + -0.611111111 = 0.326787581

Reorder the terms:
-0.611111111 + x = 0.326787581

Solving
-0.611111111 + x = 0.326787581

Solving for variable 'x'.

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

Add '0.611111111' to each side of the equation.
-0.611111111 + 0.611111111 + x = 0.326787581 + 0.611111111

Combine like terms: -0.611111111 + 0.611111111 = 0.000000000
0.000000000 + x = 0.326787581 + 0.611111111
x = 0.326787581 + 0.611111111

Combine like terms: 0.326787581 + 0.611111111 = 0.937898692
x = 0.937898692

Simplifying
x = 0.937898692


Subproblem 2
x + -0.611111111 = -0.326787581

Simplifying
x + -0.611111111 = -0.326787581

Reorder the terms:
-0.611111111 + x = -0.326787581

Solving
-0.611111111 + x = -0.326787581

Solving for variable 'x'.

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

Add '0.611111111' to each side of the equation.
-0.611111111 + 0.611111111 + x = -0.326787581 + 0.611111111

Combine like terms: -0.611111111 + 0.611111111 = 0.000000000
0.000000000 + x = -0.326787581 + 0.611111111
x = -0.326787581 + 0.611111111

Combine like terms: -0.326787581 + 0.611111111 = 0.28432353
x = 0.28432353

Simplifying
x = 0.28432353


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.937898692, 0.28432353}
Solution
x = {0.937898692, 0.28432353}

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