10x(10x-4)(10x-3)=(10x-5)(10x-1)(10x-2)

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Solution for 10x(10x-4)(10x-3)=(10x-5)(10x-1)(10x-2) equation: 


Simplifying
10x(10x + -4)(10x + -3) = (10x + -5)(10x + -1)(10x + -2)

Reorder the terms:
10x(-4 + 10x)(10x + -3) = (10x + -5)(10x + -1)(10x + -2)

Reorder the terms:
10x(-4 + 10x)(-3 + 10x) = (10x + -5)(10x + -1)(10x + -2)

Multiply (-4 + 10x) * (-3 + 10x)
10x(-4(-3 + 10x) + 10x * (-3 + 10x)) = (10x + -5)(10x + -1)(10x + -2)
10x((-3 * -4 + 10x * -4) + 10x * (-3 + 10x)) = (10x + -5)(10x + -1)(10x + -2)
10x((12 + -40x) + 10x * (-3 + 10x)) = (10x + -5)(10x + -1)(10x + -2)
10x(12 + -40x + (-3 * 10x + 10x * 10x)) = (10x + -5)(10x + -1)(10x + -2)
10x(12 + -40x + (-30x + 100x2)) = (10x + -5)(10x + -1)(10x + -2)

Combine like terms: -40x + -30x = -70x
10x(12 + -70x + 100x2) = (10x + -5)(10x + -1)(10x + -2)
(12 * 10x + -70x * 10x + 100x2 * 10x) = (10x + -5)(10x + -1)(10x + -2)
(120x + -700x2 + 1000x3) = (10x + -5)(10x + -1)(10x + -2)

Reorder the terms:
120x + -700x2 + 1000x3 = (-5 + 10x)(10x + -1)(10x + -2)

Reorder the terms:
120x + -700x2 + 1000x3 = (-5 + 10x)(-1 + 10x)(10x + -2)

Reorder the terms:
120x + -700x2 + 1000x3 = (-5 + 10x)(-1 + 10x)(-2 + 10x)

Multiply (-5 + 10x) * (-1 + 10x)
120x + -700x2 + 1000x3 = (-5(-1 + 10x) + 10x * (-1 + 10x))(-2 + 10x)
120x + -700x2 + 1000x3 = ((-1 * -5 + 10x * -5) + 10x * (-1 + 10x))(-2 + 10x)
120x + -700x2 + 1000x3 = ((5 + -50x) + 10x * (-1 + 10x))(-2 + 10x)
120x + -700x2 + 1000x3 = (5 + -50x + (-1 * 10x + 10x * 10x))(-2 + 10x)
120x + -700x2 + 1000x3 = (5 + -50x + (-10x + 100x2))(-2 + 10x)

Combine like terms: -50x + -10x = -60x
120x + -700x2 + 1000x3 = (5 + -60x + 100x2)(-2 + 10x)

Multiply (5 + -60x + 100x2) * (-2 + 10x)
120x + -700x2 + 1000x3 = (5(-2 + 10x) + -60x * (-2 + 10x) + 100x2 * (-2 + 10x))
120x + -700x2 + 1000x3 = ((-2 * 5 + 10x * 5) + -60x * (-2 + 10x) + 100x2 * (-2 + 10x))
120x + -700x2 + 1000x3 = ((-10 + 50x) + -60x * (-2 + 10x) + 100x2 * (-2 + 10x))
120x + -700x2 + 1000x3 = (-10 + 50x + (-2 * -60x + 10x * -60x) + 100x2 * (-2 + 10x))
120x + -700x2 + 1000x3 = (-10 + 50x + (120x + -600x2) + 100x2 * (-2 + 10x))
120x + -700x2 + 1000x3 = (-10 + 50x + 120x + -600x2 + (-2 * 100x2 + 10x * 100x2))
120x + -700x2 + 1000x3 = (-10 + 50x + 120x + -600x2 + (-200x2 + 1000x3))

Combine like terms: 50x + 120x = 170x
120x + -700x2 + 1000x3 = (-10 + 170x + -600x2 + -200x2 + 1000x3)

Combine like terms: -600x2 + -200x2 = -800x2
120x + -700x2 + 1000x3 = (-10 + 170x + -800x2 + 1000x3)

Add '-1000x3' to each side of the equation.
120x + -700x2 + 1000x3 + -1000x3 = -10 + 170x + -800x2 + 1000x3 + -1000x3

Combine like terms: 1000x3 + -1000x3 = 0
120x + -700x2 + 0 = -10 + 170x + -800x2 + 1000x3 + -1000x3
120x + -700x2 = -10 + 170x + -800x2 + 1000x3 + -1000x3

Combine like terms: 1000x3 + -1000x3 = 0
120x + -700x2 = -10 + 170x + -800x2 + 0
120x + -700x2 = -10 + 170x + -800x2

Solving
120x + -700x2 = -10 + 170x + -800x2

Solving for variable 'x'.

Reorder the terms:
10 + 120x + -170x + -700x2 + 800x2 = -10 + 170x + -800x2 + 10 + -170x + 800x2

Combine like terms: 120x + -170x = -50x
10 + -50x + -700x2 + 800x2 = -10 + 170x + -800x2 + 10 + -170x + 800x2

Combine like terms: -700x2 + 800x2 = 100x2
10 + -50x + 100x2 = -10 + 170x + -800x2 + 10 + -170x + 800x2

Reorder the terms:
10 + -50x + 100x2 = -10 + 10 + 170x + -170x + -800x2 + 800x2

Combine like terms: -10 + 10 = 0
10 + -50x + 100x2 = 0 + 170x + -170x + -800x2 + 800x2
10 + -50x + 100x2 = 170x + -170x + -800x2 + 800x2

Combine like terms: 170x + -170x = 0
10 + -50x + 100x2 = 0 + -800x2 + 800x2
10 + -50x + 100x2 = -800x2 + 800x2

Combine like terms: -800x2 + 800x2 = 0
10 + -50x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + -5x + 10x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(1 + -5x + 10x2)' equal to zero and attempt to solve:

Simplifying
1 + -5x + 10x2 = 0

Solving
1 + -5x + 10x2 = 0

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

Divide each side by '10'.
0.1 + -0.5x + x2 = 0.0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -0.5x + -0.1 + x2 = 0.0 + -0.1

Reorder the terms:
0.1 + -0.1 + -0.5x + x2 = 0.0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -0.5x + x2 = 0.0 + -0.1
-0.5x + x2 = 0.0 + -0.1

Combine like terms: 0.0 + -0.1 = -0.1
-0.5x + x2 = -0.1

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.1 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -0.1 + 0.0625

Combine like terms: -0.1 + 0.0625 = -0.0375
0.0625 + -0.5x + x2 = -0.0375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.0375

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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