5(a+2)(a-4)(a-5)(2a-8)=0

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Solution for 5(a+2)(a-4)(a-5)(2a-8)=0 equation: 


Simplifying
5(a + 2)(a + -4)(a + -5)(2a + -8) = 0

Reorder the terms:
5(2 + a)(a + -4)(a + -5)(2a + -8) = 0

Reorder the terms:
5(2 + a)(-4 + a)(a + -5)(2a + -8) = 0

Reorder the terms:
5(2 + a)(-4 + a)(-5 + a)(2a + -8) = 0

Reorder the terms:
5(2 + a)(-4 + a)(-5 + a)(-8 + 2a) = 0

Multiply (2 + a) * (-4 + a)
5(2(-4 + a) + a(-4 + a))(-5 + a)(-8 + 2a) = 0
5((-4 * 2 + a * 2) + a(-4 + a))(-5 + a)(-8 + 2a) = 0
5((-8 + 2a) + a(-4 + a))(-5 + a)(-8 + 2a) = 0
5(-8 + 2a + (-4 * a + a * a))(-5 + a)(-8 + 2a) = 0
5(-8 + 2a + (-4a + a2))(-5 + a)(-8 + 2a) = 0

Combine like terms: 2a + -4a = -2a
5(-8 + -2a + a2)(-5 + a)(-8 + 2a) = 0

Multiply (-8 + -2a + a2) * (-5 + a)
5(-8(-5 + a) + -2a * (-5 + a) + a2(-5 + a))(-8 + 2a) = 0
5((-5 * -8 + a * -8) + -2a * (-5 + a) + a2(-5 + a))(-8 + 2a) = 0
5((40 + -8a) + -2a * (-5 + a) + a2(-5 + a))(-8 + 2a) = 0
5(40 + -8a + (-5 * -2a + a * -2a) + a2(-5 + a))(-8 + 2a) = 0
5(40 + -8a + (10a + -2a2) + a2(-5 + a))(-8 + 2a) = 0
5(40 + -8a + 10a + -2a2 + (-5 * a2 + a * a2))(-8 + 2a) = 0
5(40 + -8a + 10a + -2a2 + (-5a2 + a3))(-8 + 2a) = 0

Combine like terms: -8a + 10a = 2a
5(40 + 2a + -2a2 + -5a2 + a3)(-8 + 2a) = 0

Combine like terms: -2a2 + -5a2 = -7a2
5(40 + 2a + -7a2 + a3)(-8 + 2a) = 0

Multiply (40 + 2a + -7a2 + a3) * (-8 + 2a)
5(40(-8 + 2a) + 2a * (-8 + 2a) + -7a2 * (-8 + 2a) + a3(-8 + 2a)) = 0
5((-8 * 40 + 2a * 40) + 2a * (-8 + 2a) + -7a2 * (-8 + 2a) + a3(-8 + 2a)) = 0
5((-320 + 80a) + 2a * (-8 + 2a) + -7a2 * (-8 + 2a) + a3(-8 + 2a)) = 0
5(-320 + 80a + (-8 * 2a + 2a * 2a) + -7a2 * (-8 + 2a) + a3(-8 + 2a)) = 0
5(-320 + 80a + (-16a + 4a2) + -7a2 * (-8 + 2a) + a3(-8 + 2a)) = 0
5(-320 + 80a + -16a + 4a2 + (-8 * -7a2 + 2a * -7a2) + a3(-8 + 2a)) = 0
5(-320 + 80a + -16a + 4a2 + (56a2 + -14a3) + a3(-8 + 2a)) = 0
5(-320 + 80a + -16a + 4a2 + 56a2 + -14a3 + (-8 * a3 + 2a * a3)) = 0
5(-320 + 80a + -16a + 4a2 + 56a2 + -14a3 + (-8a3 + 2a4)) = 0

Combine like terms: 80a + -16a = 64a
5(-320 + 64a + 4a2 + 56a2 + -14a3 + -8a3 + 2a4) = 0

Combine like terms: 4a2 + 56a2 = 60a2
5(-320 + 64a + 60a2 + -14a3 + -8a3 + 2a4) = 0

Combine like terms: -14a3 + -8a3 = -22a3
5(-320 + 64a + 60a2 + -22a3 + 2a4) = 0
(-320 * 5 + 64a * 5 + 60a2 * 5 + -22a3 * 5 + 2a4 * 5) = 0
(-1600 + 320a + 300a2 + -110a3 + 10a4) = 0

Solving
-1600 + 320a + 300a2 + -110a3 + 10a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-160 + 32a + 30a2 + -11a3 + a4) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-160 + 32a + 30a2 + -11a3 + a4)' equal to zero and attempt to solve:

Simplifying
-160 + 32a + 30a2 + -11a3 + a4 = 0

Solving
-160 + 32a + 30a2 + -11a3 + a4 = 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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