-3(2x-3)10x=33

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Solution for -3(2x-3)10x=33 equation: 


Simplifying
-3(2x + -3) * 10x = 33

Reorder the terms:
-3(-3 + 2x) * 10x = 33

Reorder the terms for easier multiplication:
-3 * 10x(-3 + 2x) = 33

Multiply -3 * 10
-30x(-3 + 2x) = 33
(-3 * -30x + 2x * -30x) = 33
(90x + -60x2) = 33

Solving
90x + -60x2 = 33

Solving for variable 'x'.

Reorder the terms:
-33 + 90x + -60x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 90x + -60x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-11 + 30x + -20x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-11 + 30x + -20x2)' equal to zero and attempt to solve:

Simplifying
-11 + 30x + -20x2 = 0

Solving
-11 + 30x + -20x2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
0.55 + -1.5x + x2 = 0.0

Move the constant term to the right:

Add '-0.55' to each side of the equation.
0.55 + -1.5x + -0.55 + x2 = 0.0 + -0.55

Reorder the terms:
0.55 + -0.55 + -1.5x + x2 = 0.0 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + -1.5x + x2 = 0.0 + -0.55
-1.5x + x2 = 0.0 + -0.55

Combine like terms: 0.0 + -0.55 = -0.55
-1.5x + x2 = -0.55

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -0.55 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -0.55 + 0.5625

Combine like terms: -0.55 + 0.5625 = 0.0125
0.5625 + -1.5x + x2 = 0.0125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 0.0125

Calculate the square root of the right side: 0.111803399

Break this problem into two subproblems by setting 
(x + -0.75) equal to 0.111803399 and -0.111803399.


Subproblem 1
x + -0.75 = 0.111803399

Simplifying
x + -0.75 = 0.111803399

Reorder the terms:
-0.75 + x = 0.111803399

Solving
-0.75 + x = 0.111803399

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 0.111803399 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 0.111803399 + 0.75
x = 0.111803399 + 0.75

Combine like terms: 0.111803399 + 0.75 = 0.861803399
x = 0.861803399

Simplifying
x = 0.861803399


Subproblem 2
x + -0.75 = -0.111803399

Simplifying
x + -0.75 = -0.111803399

Reorder the terms:
-0.75 + x = -0.111803399

Solving
-0.75 + x = -0.111803399

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -0.111803399 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -0.111803399 + 0.75
x = -0.111803399 + 0.75

Combine like terms: -0.111803399 + 0.75 = 0.638196601
x = 0.638196601

Simplifying
x = 0.638196601


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.861803399, 0.638196601}
Solution
x = {0.861803399, 0.638196601}

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