(2a+7)(2a+4)(39+1)=(1-a)(2a+7)(2a+4)

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Solution for (2a+7)(2a+4)(39+1)=(1-a)(2a+7)(2a+4) equation: 


Simplifying
(2a + 7)(2a + 4)(39 + 1) = (1 + -1a)(2a + 7)(2a + 4)

Reorder the terms:
(7 + 2a)(2a + 4)(39 + 1) = (1 + -1a)(2a + 7)(2a + 4)

Reorder the terms:
(7 + 2a)(4 + 2a)(39 + 1) = (1 + -1a)(2a + 7)(2a + 4)

Combine like terms: 39 + 1 = 40
(7 + 2a)(4 + 2a)(40) = (1 + -1a)(2a + 7)(2a + 4)

Reorder the terms for easier multiplication:
40(7 + 2a)(4 + 2a) = (1 + -1a)(2a + 7)(2a + 4)

Multiply (7 + 2a) * (4 + 2a)
40(7(4 + 2a) + 2a * (4 + 2a)) = (1 + -1a)(2a + 7)(2a + 4)
40((4 * 7 + 2a * 7) + 2a * (4 + 2a)) = (1 + -1a)(2a + 7)(2a + 4)
40((28 + 14a) + 2a * (4 + 2a)) = (1 + -1a)(2a + 7)(2a + 4)
40(28 + 14a + (4 * 2a + 2a * 2a)) = (1 + -1a)(2a + 7)(2a + 4)
40(28 + 14a + (8a + 4a2)) = (1 + -1a)(2a + 7)(2a + 4)

Combine like terms: 14a + 8a = 22a
40(28 + 22a + 4a2) = (1 + -1a)(2a + 7)(2a + 4)
(28 * 40 + 22a * 40 + 4a2 * 40) = (1 + -1a)(2a + 7)(2a + 4)
(1120 + 880a + 160a2) = (1 + -1a)(2a + 7)(2a + 4)

Reorder the terms:
1120 + 880a + 160a2 = (1 + -1a)(7 + 2a)(2a + 4)

Reorder the terms:
1120 + 880a + 160a2 = (1 + -1a)(7 + 2a)(4 + 2a)

Multiply (1 + -1a) * (7 + 2a)
1120 + 880a + 160a2 = (1(7 + 2a) + -1a * (7 + 2a))(4 + 2a)
1120 + 880a + 160a2 = ((7 * 1 + 2a * 1) + -1a * (7 + 2a))(4 + 2a)
1120 + 880a + 160a2 = ((7 + 2a) + -1a * (7 + 2a))(4 + 2a)
1120 + 880a + 160a2 = (7 + 2a + (7 * -1a + 2a * -1a))(4 + 2a)
1120 + 880a + 160a2 = (7 + 2a + (-7a + -2a2))(4 + 2a)

Combine like terms: 2a + -7a = -5a
1120 + 880a + 160a2 = (7 + -5a + -2a2)(4 + 2a)

Multiply (7 + -5a + -2a2) * (4 + 2a)
1120 + 880a + 160a2 = (7(4 + 2a) + -5a * (4 + 2a) + -2a2 * (4 + 2a))
1120 + 880a + 160a2 = ((4 * 7 + 2a * 7) + -5a * (4 + 2a) + -2a2 * (4 + 2a))
1120 + 880a + 160a2 = ((28 + 14a) + -5a * (4 + 2a) + -2a2 * (4 + 2a))
1120 + 880a + 160a2 = (28 + 14a + (4 * -5a + 2a * -5a) + -2a2 * (4 + 2a))
1120 + 880a + 160a2 = (28 + 14a + (-20a + -10a2) + -2a2 * (4 + 2a))
1120 + 880a + 160a2 = (28 + 14a + -20a + -10a2 + (4 * -2a2 + 2a * -2a2))
1120 + 880a + 160a2 = (28 + 14a + -20a + -10a2 + (-8a2 + -4a3))

Combine like terms: 14a + -20a = -6a
1120 + 880a + 160a2 = (28 + -6a + -10a2 + -8a2 + -4a3)

Combine like terms: -10a2 + -8a2 = -18a2
1120 + 880a + 160a2 = (28 + -6a + -18a2 + -4a3)

Solving
1120 + 880a + 160a2 = 28 + -6a + -18a2 + -4a3

Solving for variable 'a'.

Reorder the terms:
1120 + -28 + 880a + 6a + 160a2 + 18a2 + 4a3 = 28 + -6a + -18a2 + -4a3 + -28 + 6a + 18a2 + 4a3

Combine like terms: 1120 + -28 = 1092
1092 + 880a + 6a + 160a2 + 18a2 + 4a3 = 28 + -6a + -18a2 + -4a3 + -28 + 6a + 18a2 + 4a3

Combine like terms: 880a + 6a = 886a
1092 + 886a + 160a2 + 18a2 + 4a3 = 28 + -6a + -18a2 + -4a3 + -28 + 6a + 18a2 + 4a3

Combine like terms: 160a2 + 18a2 = 178a2
1092 + 886a + 178a2 + 4a3 = 28 + -6a + -18a2 + -4a3 + -28 + 6a + 18a2 + 4a3

Reorder the terms:
1092 + 886a + 178a2 + 4a3 = 28 + -28 + -6a + 6a + -18a2 + 18a2 + -4a3 + 4a3

Combine like terms: 28 + -28 = 0
1092 + 886a + 178a2 + 4a3 = 0 + -6a + 6a + -18a2 + 18a2 + -4a3 + 4a3
1092 + 886a + 178a2 + 4a3 = -6a + 6a + -18a2 + 18a2 + -4a3 + 4a3

Combine like terms: -6a + 6a = 0
1092 + 886a + 178a2 + 4a3 = 0 + -18a2 + 18a2 + -4a3 + 4a3
1092 + 886a + 178a2 + 4a3 = -18a2 + 18a2 + -4a3 + 4a3

Combine like terms: -18a2 + 18a2 = 0
1092 + 886a + 178a2 + 4a3 = 0 + -4a3 + 4a3
1092 + 886a + 178a2 + 4a3 = -4a3 + 4a3

Combine like terms: -4a3 + 4a3 = 0
1092 + 886a + 178a2 + 4a3 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(546 + 443a + 89a2 + 2a3) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(546 + 443a + 89a2 + 2a3)' equal to zero and attempt to solve:

Simplifying
546 + 443a + 89a2 + 2a3 = 0

Solving
546 + 443a + 89a2 + 2a3 = 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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