3(x-2)-2(3x+4)x=2

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


Simplifying
3(x + -2) + -2(3x + 4) * x = 2

Reorder the terms:
3(-2 + x) + -2(3x + 4) * x = 2
(-2 * 3 + x * 3) + -2(3x + 4) * x = 2
(-6 + 3x) + -2(3x + 4) * x = 2

Reorder the terms:
-6 + 3x + -2(4 + 3x) * x = 2

Reorder the terms for easier multiplication:
-6 + 3x + -2x(4 + 3x) = 2
-6 + 3x + (4 * -2x + 3x * -2x) = 2
-6 + 3x + (-8x + -6x2) = 2

Combine like terms: 3x + -8x = -5x
-6 + -5x + -6x2 = 2

Solving
-6 + -5x + -6x2 = 2

Solving for variable 'x'.

Reorder the terms:
-6 + -2 + -5x + -6x2 = 2 + -2

Combine like terms: -6 + -2 = -8
-8 + -5x + -6x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-8 + -5x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 5x + 6x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + 5x + 6x2)' equal to zero and attempt to solve:

Simplifying
8 + 5x + 6x2 = 0

Solving
8 + 5x + 6x2 = 0

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

Divide each side by '6'.
1.333333333 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 0.8333333333x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 0.8333333333x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 0.8333333333x + x2 = 0 + -1.333333333
0.8333333333x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
0.8333333333x + x2 = -1.333333333

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = -1.333333333 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = -1.333333333 + 0.1736111111

Combine like terms: -1.333333333 + 0.1736111111 = -1.1597222219
0.1736111111 + 0.8333333333x + x2 = -1.1597222219

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = -1.1597222219

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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