(2a+9)(6a*2-8a-2)=

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Solution for (2a+9)(6a*2-8a-2)= equation: 


Simplifying
(2a + 9)(6a * 2 + -8a + -2) = 0

Reorder the terms:
(9 + 2a)(6a * 2 + -8a + -2) = 0

Reorder the terms for easier multiplication:
(9 + 2a)(6 * 2a + -8a + -2) = 0

Multiply 6 * 2
(9 + 2a)(12a + -8a + -2) = 0

Reorder the terms:
(9 + 2a)(-2 + 12a + -8a) = 0

Combine like terms: 12a + -8a = 4a
(9 + 2a)(-2 + 4a) = 0

Multiply (9 + 2a) * (-2 + 4a)
(9(-2 + 4a) + 2a * (-2 + 4a)) = 0
((-2 * 9 + 4a * 9) + 2a * (-2 + 4a)) = 0
((-18 + 36a) + 2a * (-2 + 4a)) = 0
(-18 + 36a + (-2 * 2a + 4a * 2a)) = 0
(-18 + 36a + (-4a + 8a2)) = 0

Combine like terms: 36a + -4a = 32a
(-18 + 32a + 8a2) = 0

Solving
-18 + 32a + 8a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 16a + 4a2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -2a)' equal to zero and attempt to solve:

Simplifying
-9 + -2a = 0

Solving
-9 + -2a = 0

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

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

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

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

Divide each side by '-2'.
a = -4.5

Simplifying
a = -4.5

Subproblem 2
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
Solution
a = {-4.5, 0.5}

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