3X-4X(3-5X)-2(3X+2)=

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Solution for 3X-4X(3-5X)-2(3X+2)= equation: 


Simplifying
3X + -4X(3 + -5X) + -2(3X + 2) = 0
3X + (3 * -4X + -5X * -4X) + -2(3X + 2) = 0
3X + (-12X + 20X2) + -2(3X + 2) = 0

Reorder the terms:
3X + -12X + 20X2 + -2(2 + 3X) = 0
3X + -12X + 20X2 + (2 * -2 + 3X * -2) = 0
3X + -12X + 20X2 + (-4 + -6X) = 0

Reorder the terms:
-4 + 3X + -12X + -6X + 20X2 = 0

Combine like terms: 3X + -12X = -9X
-4 + -9X + -6X + 20X2 = 0

Combine like terms: -9X + -6X = -15X
-4 + -15X + 20X2 = 0

Solving
-4 + -15X + 20X2 = 0

Solving for variable 'X'.

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

Divide each side by '20'.
-0.2 + -0.75X + X2 = 0.0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.75X + 0.2 + X2 = 0.0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.75X + X2 = 0.0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.75X + X2 = 0.0 + 0.2
-0.75X + X2 = 0.0 + 0.2

Combine like terms: 0.0 + 0.2 = 0.2
-0.75X + X2 = 0.2

The X term is -0.75X.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75X + 0.140625 + X2 = 0.2 + 0.140625

Reorder the terms:
0.140625 + -0.75X + X2 = 0.2 + 0.140625

Combine like terms: 0.2 + 0.140625 = 0.340625
0.140625 + -0.75X + X2 = 0.340625

Factor a perfect square on the left side:
(X + -0.375)(X + -0.375) = 0.340625

Calculate the square root of the right side: 0.583630876

Break this problem into two subproblems by setting 
(X + -0.375) equal to 0.583630876 and -0.583630876.


Subproblem 1
X + -0.375 = 0.583630876

Simplifying
X + -0.375 = 0.583630876

Reorder the terms:
-0.375 + X = 0.583630876

Solving
-0.375 + X = 0.583630876

Solving for variable 'X'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + X = 0.583630876 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + X = 0.583630876 + 0.375
X = 0.583630876 + 0.375

Combine like terms: 0.583630876 + 0.375 = 0.958630876
X = 0.958630876

Simplifying
X = 0.958630876


Subproblem 2
X + -0.375 = -0.583630876

Simplifying
X + -0.375 = -0.583630876

Reorder the terms:
-0.375 + X = -0.583630876

Solving
-0.375 + X = -0.583630876

Solving for variable 'X'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + X = -0.583630876 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + X = -0.583630876 + 0.375
X = -0.583630876 + 0.375

Combine like terms: -0.583630876 + 0.375 = -0.208630876
X = -0.208630876

Simplifying
X = -0.208630876


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.958630876, -0.208630876}

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