a=.5((9a)(10+4c))

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Solution for a=.5((9a)(10+4c)) equation: 


Simplifying
a = 0.5((9a)(10 + 4c))

Remove parenthesis around (9a)
a = 0.5(9a(10 + 4c))
a = 0.5((10 * 9a + 4c * 9a))
a = 0.5((90a + 36ac))
a = (90a * 0.5 + 36ac * 0.5)
a = (45a + 18ac)

Solving
a = 45a + 18ac

Solving for variable 'a'.

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

Add '-45a' to each side of the equation.
a + -45a = 45a + -45a + 18ac

Combine like terms: a + -45a = -44a
-44a = 45a + -45a + 18ac

Combine like terms: 45a + -45a = 0
-44a = 0 + 18ac
-44a = 18ac

Add '-18ac' to each side of the equation.
-44a + -18ac = 18ac + -18ac

Combine like terms: 18ac + -18ac = 0
-44a + -18ac = 0

Factor out the Greatest Common Factor (GCF), '-2a'.
-2a(22 + 9c) = 0

Ignore the factor -2.

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(22 + 9c)' equal to zero and attempt to solve:

Simplifying
22 + 9c = 0

Solving
22 + 9c = 0

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

Add '-22' to each side of the equation.
22 + -22 + 9c = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 9c = 0 + -22
9c = 0 + -22

Combine like terms: 0 + -22 = -22
9c = -22

Add '-9c' to each side of the equation.
9c + -9c = -22 + -9c

Combine like terms: 9c + -9c = 0
0 = -22 + -9c

Simplifying
0 = -22 + -9c

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}

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