7(14a+7w)8(7a+9w)=

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Solution for 7(14a+7w)8(7a+9w)= equation: 


Simplifying
7(14a + 7w) * 8(7a + 9w) = 0

Reorder the terms for easier multiplication:
7 * 8(14a + 7w)(7a + 9w) = 0

Multiply 7 * 8
56(14a + 7w)(7a + 9w) = 0

Multiply (14a + 7w) * (7a + 9w)
56(14a * (7a + 9w) + 7w * (7a + 9w)) = 0
56((7a * 14a + 9w * 14a) + 7w * (7a + 9w)) = 0

Reorder the terms:
56((126aw + 98a2) + 7w * (7a + 9w)) = 0
56((126aw + 98a2) + 7w * (7a + 9w)) = 0
56(126aw + 98a2 + (7a * 7w + 9w * 7w)) = 0
56(126aw + 98a2 + (49aw + 63w2)) = 0

Reorder the terms:
56(126aw + 49aw + 98a2 + 63w2) = 0

Combine like terms: 126aw + 49aw = 175aw
56(175aw + 98a2 + 63w2) = 0
(175aw * 56 + 98a2 * 56 + 63w2 * 56) = 0
(9800aw + 5488a2 + 3528w2) = 0

Solving
9800aw + 5488a2 + 3528w2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '392'.
392(25aw + 14a2 + 9w2) = 0

Factor a trinomial.
392((2a + w)(7a + 9w)) = 0

Ignore the factor 392.

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

Simplifying
2a + w = 0

Solving
2a + w = 0

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

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

Combine like terms: w + -1w = 0
2a + 0 = 0 + -1w
2a = 0 + -1w
Remove the zero:
2a = -1w

Divide each side by '2'.
a = -0.5w

Simplifying
a = -0.5w

Subproblem 2
Set the factor '(7a + 9w)' equal to zero and attempt to solve:

Simplifying
7a + 9w = 0

Solving
7a + 9w = 0

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

Add '-9w' to each side of the equation.
7a + 9w + -9w = 0 + -9w

Combine like terms: 9w + -9w = 0
7a + 0 = 0 + -9w
7a = 0 + -9w
Remove the zero:
7a = -9w

Divide each side by '7'.
a = -1.285714286w

Simplifying
a = -1.285714286w
Solution
a = {-0.5w, -1.285714286w}

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