(a+2)(a-4)+10=(-a-2)(6-a)

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Solution for (a+2)(a-4)+10=(-a-2)(6-a) equation: 


Simplifying
(a + 2)(a + -4) + 10 = (-1a + -2)(6 + -1a)

Reorder the terms:
(2 + a)(a + -4) + 10 = (-1a + -2)(6 + -1a)

Reorder the terms:
(2 + a)(-4 + a) + 10 = (-1a + -2)(6 + -1a)

Multiply (2 + a) * (-4 + a)
(2(-4 + a) + a(-4 + a)) + 10 = (-1a + -2)(6 + -1a)
((-4 * 2 + a * 2) + a(-4 + a)) + 10 = (-1a + -2)(6 + -1a)
((-8 + 2a) + a(-4 + a)) + 10 = (-1a + -2)(6 + -1a)
(-8 + 2a + (-4 * a + a * a)) + 10 = (-1a + -2)(6 + -1a)
(-8 + 2a + (-4a + a2)) + 10 = (-1a + -2)(6 + -1a)

Combine like terms: 2a + -4a = -2a
(-8 + -2a + a2) + 10 = (-1a + -2)(6 + -1a)

Reorder the terms:
-8 + 10 + -2a + a2 = (-1a + -2)(6 + -1a)

Combine like terms: -8 + 10 = 2
2 + -2a + a2 = (-1a + -2)(6 + -1a)

Reorder the terms:
2 + -2a + a2 = (-2 + -1a)(6 + -1a)

Multiply (-2 + -1a) * (6 + -1a)
2 + -2a + a2 = (-2(6 + -1a) + -1a * (6 + -1a))
2 + -2a + a2 = ((6 * -2 + -1a * -2) + -1a * (6 + -1a))
2 + -2a + a2 = ((-12 + 2a) + -1a * (6 + -1a))
2 + -2a + a2 = (-12 + 2a + (6 * -1a + -1a * -1a))
2 + -2a + a2 = (-12 + 2a + (-6a + 1a2))

Combine like terms: 2a + -6a = -4a
2 + -2a + a2 = (-12 + -4a + 1a2)

Solving
2 + -2a + a2 = -12 + -4a + 1a2

Solving for variable 'a'.

Reorder the terms:
2 + 12 + -2a + 4a + a2 + -1a2 = -12 + -4a + 1a2 + 12 + 4a + -1a2

Combine like terms: 2 + 12 = 14
14 + -2a + 4a + a2 + -1a2 = -12 + -4a + 1a2 + 12 + 4a + -1a2

Combine like terms: -2a + 4a = 2a
14 + 2a + a2 + -1a2 = -12 + -4a + 1a2 + 12 + 4a + -1a2

Combine like terms: a2 + -1a2 = 0
14 + 2a + 0 = -12 + -4a + 1a2 + 12 + 4a + -1a2
14 + 2a = -12 + -4a + 1a2 + 12 + 4a + -1a2

Reorder the terms:
14 + 2a = -12 + 12 + -4a + 4a + 1a2 + -1a2

Combine like terms: -12 + 12 = 0
14 + 2a = 0 + -4a + 4a + 1a2 + -1a2
14 + 2a = -4a + 4a + 1a2 + -1a2

Combine like terms: -4a + 4a = 0
14 + 2a = 0 + 1a2 + -1a2
14 + 2a = 1a2 + -1a2

Combine like terms: 1a2 + -1a2 = 0
14 + 2a = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + a) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + a)' equal to zero and attempt to solve:

Simplifying
7 + a = 0

Solving
7 + a = 0

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

Add '-7' to each side of the equation.
7 + -7 + a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + a = 0 + -7
a = 0 + -7

Combine like terms: 0 + -7 = -7
a = -7

Simplifying
a = -7
Solution
a = {-7}

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