2(4-3x)5(2x-3)=20-5x

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Solution for 2(4-3x)5(2x-3)=20-5x equation: 


Simplifying
2(4 + -3x) * 5(2x + -3) = 20 + -5x

Reorder the terms:
2(4 + -3x) * 5(-3 + 2x) = 20 + -5x

Reorder the terms for easier multiplication:
2 * 5(4 + -3x)(-3 + 2x) = 20 + -5x

Multiply 2 * 5
10(4 + -3x)(-3 + 2x) = 20 + -5x

Multiply (4 + -3x) * (-3 + 2x)
10(4(-3 + 2x) + -3x * (-3 + 2x)) = 20 + -5x
10((-3 * 4 + 2x * 4) + -3x * (-3 + 2x)) = 20 + -5x
10((-12 + 8x) + -3x * (-3 + 2x)) = 20 + -5x
10(-12 + 8x + (-3 * -3x + 2x * -3x)) = 20 + -5x
10(-12 + 8x + (9x + -6x2)) = 20 + -5x

Combine like terms: 8x + 9x = 17x
10(-12 + 17x + -6x2) = 20 + -5x
(-12 * 10 + 17x * 10 + -6x2 * 10) = 20 + -5x
(-120 + 170x + -60x2) = 20 + -5x

Solving
-120 + 170x + -60x2 = 20 + -5x

Solving for variable 'x'.

Reorder the terms:
-120 + -20 + 170x + 5x + -60x2 = 20 + -5x + -20 + 5x

Combine like terms: -120 + -20 = -140
-140 + 170x + 5x + -60x2 = 20 + -5x + -20 + 5x

Combine like terms: 170x + 5x = 175x
-140 + 175x + -60x2 = 20 + -5x + -20 + 5x

Reorder the terms:
-140 + 175x + -60x2 = 20 + -20 + -5x + 5x

Combine like terms: 20 + -20 = 0
-140 + 175x + -60x2 = 0 + -5x + 5x
-140 + 175x + -60x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-140 + 175x + -60x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-28 + 35x + -12x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-28 + 35x + -12x2)' equal to zero and attempt to solve:

Simplifying
-28 + 35x + -12x2 = 0

Solving
-28 + 35x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
2.333333333 + -2.916666667x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -2.916666667x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -2.916666667x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -2.916666667x + x2 = 0 + -2.333333333
-2.916666667x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-2.916666667x + x2 = -2.333333333

The x term is -2.916666667x.  Take half its coefficient (-1.458333334).
Square it (2.126736113) and add it to both sides.

Add '2.126736113' to each side of the equation.
-2.916666667x + 2.126736113 + x2 = -2.333333333 + 2.126736113

Reorder the terms:
2.126736113 + -2.916666667x + x2 = -2.333333333 + 2.126736113

Combine like terms: -2.333333333 + 2.126736113 = -0.20659722
2.126736113 + -2.916666667x + x2 = -0.20659722

Factor a perfect square on the left side:
(x + -1.458333334)(x + -1.458333334) = -0.20659722

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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