(4x+5)(10x-3)(15x-4)=x

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Solution for (4x+5)(10x-3)(15x-4)=x equation: 


Simplifying
(4x + 5)(10x + -3)(15x + -4) = x

Reorder the terms:
(5 + 4x)(10x + -3)(15x + -4) = x

Reorder the terms:
(5 + 4x)(-3 + 10x)(15x + -4) = x

Reorder the terms:
(5 + 4x)(-3 + 10x)(-4 + 15x) = x

Multiply (5 + 4x) * (-3 + 10x)
(5(-3 + 10x) + 4x * (-3 + 10x))(-4 + 15x) = x
((-3 * 5 + 10x * 5) + 4x * (-3 + 10x))(-4 + 15x) = x
((-15 + 50x) + 4x * (-3 + 10x))(-4 + 15x) = x
(-15 + 50x + (-3 * 4x + 10x * 4x))(-4 + 15x) = x
(-15 + 50x + (-12x + 40x2))(-4 + 15x) = x

Combine like terms: 50x + -12x = 38x
(-15 + 38x + 40x2)(-4 + 15x) = x

Multiply (-15 + 38x + 40x2) * (-4 + 15x)
(-15(-4 + 15x) + 38x * (-4 + 15x) + 40x2 * (-4 + 15x)) = x
((-4 * -15 + 15x * -15) + 38x * (-4 + 15x) + 40x2 * (-4 + 15x)) = x
((60 + -225x) + 38x * (-4 + 15x) + 40x2 * (-4 + 15x)) = x
(60 + -225x + (-4 * 38x + 15x * 38x) + 40x2 * (-4 + 15x)) = x
(60 + -225x + (-152x + 570x2) + 40x2 * (-4 + 15x)) = x
(60 + -225x + -152x + 570x2 + (-4 * 40x2 + 15x * 40x2)) = x
(60 + -225x + -152x + 570x2 + (-160x2 + 600x3)) = x

Combine like terms: -225x + -152x = -377x
(60 + -377x + 570x2 + -160x2 + 600x3) = x

Combine like terms: 570x2 + -160x2 = 410x2
(60 + -377x + 410x2 + 600x3) = x

Solving
60 + -377x + 410x2 + 600x3 = x

Solving for variable 'x'.

Reorder the terms:
60 + -377x + -1x + 410x2 + 600x3 = x + -1x

Combine like terms: -377x + -1x = -378x
60 + -378x + 410x2 + 600x3 = x + -1x

Combine like terms: x + -1x = 0
60 + -378x + 410x2 + 600x3 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -189x + 205x2 + 300x3) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(30 + -189x + 205x2 + 300x3)' equal to zero and attempt to solve:

Simplifying
30 + -189x + 205x2 + 300x3 = 0

Solving
30 + -189x + 205x2 + 300x3 = 0

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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