(9a-2)(4a+8)=0

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Solution for (9a-2)(4a+8)=0 equation: 


Simplifying
(9a + -2)(4a + 8) = 0

Reorder the terms:
(-2 + 9a)(4a + 8) = 0

Reorder the terms:
(-2 + 9a)(8 + 4a) = 0

Multiply (-2 + 9a) * (8 + 4a)
(-2(8 + 4a) + 9a * (8 + 4a)) = 0
((8 * -2 + 4a * -2) + 9a * (8 + 4a)) = 0
((-16 + -8a) + 9a * (8 + 4a)) = 0
(-16 + -8a + (8 * 9a + 4a * 9a)) = 0
(-16 + -8a + (72a + 36a2)) = 0

Combine like terms: -8a + 72a = 64a
(-16 + 64a + 36a2) = 0

Solving
-16 + 64a + 36a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 16a + 9a2) = 0

Factor a trinomial.
4((-2 + -1a)(2 + -9a)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = -2

Simplifying
a = -2

Subproblem 2
Set the factor '(2 + -9a)' equal to zero and attempt to solve:

Simplifying
2 + -9a = 0

Solving
2 + -9a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -9a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9a = 0 + -2
-9a = 0 + -2

Combine like terms: 0 + -2 = -2
-9a = -2

Divide each side by '-9'.
a = 0.2222222222

Simplifying
a = 0.2222222222
Solution
a = {-2, 0.2222222222}

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