(x-4)(x-5)(x-8)(x-10)=72x^2

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Solution for (x-4)(x-5)(x-8)(x-10)=72x^2 equation: 


Simplifying
(x + -4)(x + -5)(x + -8)(x + -10) = 72x2

Reorder the terms:
(-4 + x)(x + -5)(x + -8)(x + -10) = 72x2

Reorder the terms:
(-4 + x)(-5 + x)(x + -8)(x + -10) = 72x2

Reorder the terms:
(-4 + x)(-5 + x)(-8 + x)(x + -10) = 72x2

Reorder the terms:
(-4 + x)(-5 + x)(-8 + x)(-10 + x) = 72x2

Multiply (-4 + x) * (-5 + x)
(-4(-5 + x) + x(-5 + x))(-8 + x)(-10 + x) = 72x2
((-5 * -4 + x * -4) + x(-5 + x))(-8 + x)(-10 + x) = 72x2
((20 + -4x) + x(-5 + x))(-8 + x)(-10 + x) = 72x2
(20 + -4x + (-5 * x + x * x))(-8 + x)(-10 + x) = 72x2
(20 + -4x + (-5x + x2))(-8 + x)(-10 + x) = 72x2

Combine like terms: -4x + -5x = -9x
(20 + -9x + x2)(-8 + x)(-10 + x) = 72x2

Multiply (20 + -9x + x2) * (-8 + x)
(20(-8 + x) + -9x * (-8 + x) + x2(-8 + x))(-10 + x) = 72x2
((-8 * 20 + x * 20) + -9x * (-8 + x) + x2(-8 + x))(-10 + x) = 72x2
((-160 + 20x) + -9x * (-8 + x) + x2(-8 + x))(-10 + x) = 72x2
(-160 + 20x + (-8 * -9x + x * -9x) + x2(-8 + x))(-10 + x) = 72x2
(-160 + 20x + (72x + -9x2) + x2(-8 + x))(-10 + x) = 72x2
(-160 + 20x + 72x + -9x2 + (-8 * x2 + x * x2))(-10 + x) = 72x2
(-160 + 20x + 72x + -9x2 + (-8x2 + x3))(-10 + x) = 72x2

Combine like terms: 20x + 72x = 92x
(-160 + 92x + -9x2 + -8x2 + x3)(-10 + x) = 72x2

Combine like terms: -9x2 + -8x2 = -17x2
(-160 + 92x + -17x2 + x3)(-10 + x) = 72x2

Multiply (-160 + 92x + -17x2 + x3) * (-10 + x)
(-160(-10 + x) + 92x * (-10 + x) + -17x2 * (-10 + x) + x3(-10 + x)) = 72x2
((-10 * -160 + x * -160) + 92x * (-10 + x) + -17x2 * (-10 + x) + x3(-10 + x)) = 72x2
((1600 + -160x) + 92x * (-10 + x) + -17x2 * (-10 + x) + x3(-10 + x)) = 72x2
(1600 + -160x + (-10 * 92x + x * 92x) + -17x2 * (-10 + x) + x3(-10 + x)) = 72x2
(1600 + -160x + (-920x + 92x2) + -17x2 * (-10 + x) + x3(-10 + x)) = 72x2
(1600 + -160x + -920x + 92x2 + (-10 * -17x2 + x * -17x2) + x3(-10 + x)) = 72x2
(1600 + -160x + -920x + 92x2 + (170x2 + -17x3) + x3(-10 + x)) = 72x2
(1600 + -160x + -920x + 92x2 + 170x2 + -17x3 + (-10 * x3 + x * x3)) = 72x2
(1600 + -160x + -920x + 92x2 + 170x2 + -17x3 + (-10x3 + x4)) = 72x2

Combine like terms: -160x + -920x = -1080x
(1600 + -1080x + 92x2 + 170x2 + -17x3 + -10x3 + x4) = 72x2

Combine like terms: 92x2 + 170x2 = 262x2
(1600 + -1080x + 262x2 + -17x3 + -10x3 + x4) = 72x2

Combine like terms: -17x3 + -10x3 = -27x3
(1600 + -1080x + 262x2 + -27x3 + x4) = 72x2

Solving
1600 + -1080x + 262x2 + -27x3 + x4 = 72x2

Solving for variable 'x'.

Reorder the terms:
1600 + -1080x + 262x2 + -72x2 + -27x3 + x4 = 72x2 + -72x2

Combine like terms: 262x2 + -72x2 = 190x2
1600 + -1080x + 190x2 + -27x3 + x4 = 72x2 + -72x2

Combine like terms: 72x2 + -72x2 = 0
1600 + -1080x + 190x2 + -27x3 + x4 = 0

The solution to this equation could not be determined.

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