(4a-3)(4a-3)(4a-3)-(5-4a)(8a+1)-2(2a-3)(8a(2a-1)+5)=

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Solution for (4a-3)(4a-3)(4a-3)-(5-4a)(8a+1)-2(2a-3)(8a(2a-1)+5)= equation: 


Simplifying
(4a + -3)(4a + -3)(4a + -3) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Reorder the terms:
(-3 + 4a)(4a + -3)(4a + -3) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Reorder the terms:
(-3 + 4a)(-3 + 4a)(4a + -3) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Reorder the terms:
(-3 + 4a)(-3 + 4a)(-3 + 4a) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Multiply (-3 + 4a) * (-3 + 4a)
(-3(-3 + 4a) + 4a * (-3 + 4a))(-3 + 4a) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0
((-3 * -3 + 4a * -3) + 4a * (-3 + 4a))(-3 + 4a) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0
((9 + -12a) + 4a * (-3 + 4a))(-3 + 4a) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0
(9 + -12a + (-3 * 4a + 4a * 4a))(-3 + 4a) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0
(9 + -12a + (-12a + 16a2))(-3 + 4a) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Combine like terms: -12a + -12a = -24a
(9 + -24a + 16a2)(-3 + 4a) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Multiply (9 + -24a + 16a2) * (-3 + 4a)
(9(-3 + 4a) + -24a * (-3 + 4a) + 16a2 * (-3 + 4a)) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0
((-3 * 9 + 4a * 9) + -24a * (-3 + 4a) + 16a2 * (-3 + 4a)) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0
((-27 + 36a) + -24a * (-3 + 4a) + 16a2 * (-3 + 4a)) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0
(-27 + 36a + (-3 * -24a + 4a * -24a) + 16a2 * (-3 + 4a)) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0
(-27 + 36a + (72a + -96a2) + 16a2 * (-3 + 4a)) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0
(-27 + 36a + 72a + -96a2 + (-3 * 16a2 + 4a * 16a2)) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0
(-27 + 36a + 72a + -96a2 + (-48a2 + 64a3)) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Combine like terms: 36a + 72a = 108a
(-27 + 108a + -96a2 + -48a2 + 64a3) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Combine like terms: -96a2 + -48a2 = -144a2
(-27 + 108a + -144a2 + 64a3) + -1(5 + -4a)(8a + 1) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Reorder the terms:
-27 + 108a + -144a2 + 64a3 + -1(5 + -4a)(1 + 8a) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Multiply (5 + -4a) * (1 + 8a)
-27 + 108a + -144a2 + 64a3 + -1(5(1 + 8a) + -4a * (1 + 8a)) + -2(2a + -3)(8a(2a + -1) + 5) = 0
-27 + 108a + -144a2 + 64a3 + -1((1 * 5 + 8a * 5) + -4a * (1 + 8a)) + -2(2a + -3)(8a(2a + -1) + 5) = 0
-27 + 108a + -144a2 + 64a3 + -1((5 + 40a) + -4a * (1 + 8a)) + -2(2a + -3)(8a(2a + -1) + 5) = 0
-27 + 108a + -144a2 + 64a3 + -1(5 + 40a + (1 * -4a + 8a * -4a)) + -2(2a + -3)(8a(2a + -1) + 5) = 0
-27 + 108a + -144a2 + 64a3 + -1(5 + 40a + (-4a + -32a2)) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Combine like terms: 40a + -4a = 36a
-27 + 108a + -144a2 + 64a3 + -1(5 + 36a + -32a2) + -2(2a + -3)(8a(2a + -1) + 5) = 0
-27 + 108a + -144a2 + 64a3 + (5 * -1 + 36a * -1 + -32a2 * -1) + -2(2a + -3)(8a(2a + -1) + 5) = 0
-27 + 108a + -144a2 + 64a3 + (-5 + -36a + 32a2) + -2(2a + -3)(8a(2a + -1) + 5) = 0

Reorder the terms:
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2(-3 + 2a)(8a(2a + -1) + 5) = 0

Reorder the terms:
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2(-3 + 2a)(8a(-1 + 2a) + 5) = 0
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2(-3 + 2a)((-1 * 8a + 2a * 8a) + 5) = 0
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2(-3 + 2a)((-8a + 16a2) + 5) = 0

Reorder the terms:
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2(-3 + 2a)(5 + -8a + 16a2) = 0

Multiply (-3 + 2a) * (5 + -8a + 16a2)
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2(-3(5 + -8a + 16a2) + 2a * (5 + -8a + 16a2)) = 0
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2((5 * -3 + -8a * -3 + 16a2 * -3) + 2a * (5 + -8a + 16a2)) = 0
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2((-15 + 24a + -48a2) + 2a * (5 + -8a + 16a2)) = 0
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2(-15 + 24a + -48a2 + (5 * 2a + -8a * 2a + 16a2 * 2a)) = 0
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2(-15 + 24a + -48a2 + (10a + -16a2 + 32a3)) = 0

Reorder the terms:
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2(-15 + 24a + 10a + -48a2 + -16a2 + 32a3) = 0

Combine like terms: 24a + 10a = 34a
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2(-15 + 34a + -48a2 + -16a2 + 32a3) = 0

Combine like terms: -48a2 + -16a2 = -64a2
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + -2(-15 + 34a + -64a2 + 32a3) = 0
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + (-15 * -2 + 34a * -2 + -64a2 * -2 + 32a3 * -2) = 0
-27 + 108a + -144a2 + 64a3 + -5 + -36a + 32a2 + (30 + -68a + 128a2 + -64a3) = 0

Reorder the terms:
-27 + -5 + 30 + 108a + -36a + -68a + -144a2 + 32a2 + 128a2 + 64a3 + -64a3 = 0

Combine like terms: -27 + -5 = -32
-32 + 30 + 108a + -36a + -68a + -144a2 + 32a2 + 128a2 + 64a3 + -64a3 = 0

Combine like terms: -32 + 30 = -2
-2 + 108a + -36a + -68a + -144a2 + 32a2 + 128a2 + 64a3 + -64a3 = 0

Combine like terms: 108a + -36a = 72a
-2 + 72a + -68a + -144a2 + 32a2 + 128a2 + 64a3 + -64a3 = 0

Combine like terms: 72a + -68a = 4a
-2 + 4a + -144a2 + 32a2 + 128a2 + 64a3 + -64a3 = 0

Combine like terms: -144a2 + 32a2 = -112a2
-2 + 4a + -112a2 + 128a2 + 64a3 + -64a3 = 0

Combine like terms: -112a2 + 128a2 = 16a2
-2 + 4a + 16a2 + 64a3 + -64a3 = 0

Combine like terms: 64a3 + -64a3 = 0
-2 + 4a + 16a2 + 0 = 0
-2 + 4a + 16a2 = 0

Solving
-2 + 4a + 16a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 2a + 8a2) = 0

Factor a trinomial.
2((-1 + -2a)(1 + -4a)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -2a)' equal to zero and attempt to solve:

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 0

Move all terms containing a to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -2a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a = 0 + 1
-2a = 0 + 1

Combine like terms: 0 + 1 = 1
-2a = 1

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5

Subproblem 2
Set the factor '(1 + -4a)' equal to zero and attempt to solve:

Simplifying
1 + -4a = 0

Solving
1 + -4a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -4a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4a = 0 + -1
-4a = 0 + -1

Combine like terms: 0 + -1 = -1
-4a = -1

Divide each side by '-4'.
a = 0.25

Simplifying
a = 0.25
Solution
a = {-0.5, 0.25}

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