-4a(a-13)=8(a+12)

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Solution for -4a(a-13)=8(a+12) equation: 


Simplifying
-4a(a + -13) = 8(a + 12)

Reorder the terms:
-4a(-13 + a) = 8(a + 12)
(-13 * -4a + a * -4a) = 8(a + 12)
(52a + -4a2) = 8(a + 12)

Reorder the terms:
52a + -4a2 = 8(12 + a)
52a + -4a2 = (12 * 8 + a * 8)
52a + -4a2 = (96 + 8a)

Solving
52a + -4a2 = 96 + 8a

Solving for variable 'a'.

Reorder the terms:
-96 + 52a + -8a + -4a2 = 96 + 8a + -96 + -8a

Combine like terms: 52a + -8a = 44a
-96 + 44a + -4a2 = 96 + 8a + -96 + -8a

Reorder the terms:
-96 + 44a + -4a2 = 96 + -96 + 8a + -8a

Combine like terms: 96 + -96 = 0
-96 + 44a + -4a2 = 0 + 8a + -8a
-96 + 44a + -4a2 = 8a + -8a

Combine like terms: 8a + -8a = 0
-96 + 44a + -4a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + 11a + -1a2) = 0

Factor a trinomial.
4((-8 + a)(3 + -1a)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-8 + a)' equal to zero and attempt to solve:

Simplifying
-8 + a = 0

Solving
-8 + a = 0

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

Add '8' to each side of the equation.
-8 + 8 + a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + a = 0 + 8
a = 0 + 8

Combine like terms: 0 + 8 = 8
a = 8

Simplifying
a = 8

Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {8, 3}

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