7(9a+8w)9(6a-4w)=

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Solution for 7(9a+8w)9(6a-4w)= equation: 


Simplifying
7(9a + 8w) * 9(6a + -4w) = 0

Reorder the terms for easier multiplication:
7 * 9(9a + 8w)(6a + -4w) = 0

Multiply 7 * 9
63(9a + 8w)(6a + -4w) = 0

Multiply (9a + 8w) * (6a + -4w)
63(9a * (6a + -4w) + 8w * (6a + -4w)) = 0
63((6a * 9a + -4w * 9a) + 8w * (6a + -4w)) = 0

Reorder the terms:
63((-36aw + 54a2) + 8w * (6a + -4w)) = 0
63((-36aw + 54a2) + 8w * (6a + -4w)) = 0
63(-36aw + 54a2 + (6a * 8w + -4w * 8w)) = 0
63(-36aw + 54a2 + (48aw + -32w2)) = 0

Reorder the terms:
63(-36aw + 48aw + 54a2 + -32w2) = 0

Combine like terms: -36aw + 48aw = 12aw
63(12aw + 54a2 + -32w2) = 0
(12aw * 63 + 54a2 * 63 + -32w2 * 63) = 0
(756aw + 3402a2 + -2016w2) = 0

Solving
756aw + 3402a2 + -2016w2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '126'.
126(6aw + 27a2 + -16w2) = 0

Factor a trinomial.
126((3a + -2w)(9a + 8w)) = 0

Ignore the factor 126.

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

Simplifying
3a + -2w = 0

Solving
3a + -2w = 0

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

Add '2w' to each side of the equation.
3a + -2w + 2w = 0 + 2w

Combine like terms: -2w + 2w = 0
3a + 0 = 0 + 2w
3a = 0 + 2w
Remove the zero:
3a = 2w

Divide each side by '3'.
a = 0.6666666667w

Simplifying
a = 0.6666666667w

Subproblem 2
Set the factor '(9a + 8w)' equal to zero and attempt to solve:

Simplifying
9a + 8w = 0

Solving
9a + 8w = 0

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

Add '-8w' to each side of the equation.
9a + 8w + -8w = 0 + -8w

Combine like terms: 8w + -8w = 0
9a + 0 = 0 + -8w
9a = 0 + -8w
Remove the zero:
9a = -8w

Divide each side by '9'.
a = -0.8888888889w

Simplifying
a = -0.8888888889w
Solution
a = {0.6666666667w, -0.8888888889w}

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