(2-3x)(3x-10)-(3x-1)(8)=0

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Solution for (2-3x)(3x-10)-(3x-1)(8)=0 equation: 


Simplifying
(2 + -3x)(3x + -10) + -1(3x + -1)(8) = 0

Reorder the terms:
(2 + -3x)(-10 + 3x) + -1(3x + -1)(8) = 0

Multiply (2 + -3x) * (-10 + 3x)
(2(-10 + 3x) + -3x * (-10 + 3x)) + -1(3x + -1)(8) = 0
((-10 * 2 + 3x * 2) + -3x * (-10 + 3x)) + -1(3x + -1)(8) = 0
((-20 + 6x) + -3x * (-10 + 3x)) + -1(3x + -1)(8) = 0
(-20 + 6x + (-10 * -3x + 3x * -3x)) + -1(3x + -1)(8) = 0
(-20 + 6x + (30x + -9x2)) + -1(3x + -1)(8) = 0

Combine like terms: 6x + 30x = 36x
(-20 + 36x + -9x2) + -1(3x + -1)(8) = 0

Reorder the terms:
-20 + 36x + -9x2 + -1(-1 + 3x)(8) = 0

Reorder the terms for easier multiplication:
-20 + 36x + -9x2 + -1 * 8(-1 + 3x) = 0

Multiply -1 * 8
-20 + 36x + -9x2 + -8(-1 + 3x) = 0
-20 + 36x + -9x2 + (-1 * -8 + 3x * -8) = 0
-20 + 36x + -9x2 + (8 + -24x) = 0

Reorder the terms:
-20 + 8 + 36x + -24x + -9x2 = 0

Combine like terms: -20 + 8 = -12
-12 + 36x + -24x + -9x2 = 0

Combine like terms: 36x + -24x = 12x
-12 + 12x + -9x2 = 0

Solving
-12 + 12x + -9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 4x + -3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + 4x + -3x2)' equal to zero and attempt to solve:

Simplifying
-4 + 4x + -3x2 = 0

Solving
-4 + 4x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
1.333333333 + -1.333333333x + x2 = 0

Move the constant term to the right:

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

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

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

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

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = -1.333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = -1.333333333 + 0.4444444442

Combine like terms: -1.333333333 + 0.4444444442 = -0.8888888888
0.4444444442 + -1.333333333x + x2 = -0.8888888888

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = -0.8888888888

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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