7a(10a-9c)(10a+9c)=

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Solution for 7a(10a-9c)(10a+9c)= equation: 


Simplifying
7a(10a + -9c)(10a + 9c) = 0

Multiply (10a + -9c) * (10a + 9c)
7a(10a * (10a + 9c) + -9c * (10a + 9c)) = 0
7a((10a * 10a + 9c * 10a) + -9c * (10a + 9c)) = 0

Reorder the terms:
7a((90ac + 100a2) + -9c * (10a + 9c)) = 0
7a((90ac + 100a2) + -9c * (10a + 9c)) = 0
7a(90ac + 100a2 + (10a * -9c + 9c * -9c)) = 0
7a(90ac + 100a2 + (-90ac + -81c2)) = 0

Reorder the terms:
7a(90ac + -90ac + 100a2 + -81c2) = 0

Combine like terms: 90ac + -90ac = 0
7a(0 + 100a2 + -81c2) = 0
7a(100a2 + -81c2) = 0
(100a2 * 7a + -81c2 * 7a) = 0

Reorder the terms:
(-567ac2 + 700a3) = 0
(-567ac2 + 700a3) = 0

Solving
-567ac2 + 700a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '7a'.
7a(-81c2 + 100a2) = 0

Factor a difference between two squares.
7a((9c + 10a)(-9c + 10a)) = 0

Ignore the factor 7.

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 '(9c + 10a)' equal to zero and attempt to solve:

Simplifying
9c + 10a = 0

Reorder the terms:
10a + 9c = 0

Solving
10a + 9c = 0

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

Add '-9c' to each side of the equation.
10a + 9c + -9c = 0 + -9c

Combine like terms: 9c + -9c = 0
10a + 0 = 0 + -9c
10a = 0 + -9c
Remove the zero:
10a = -9c

Divide each side by '10'.
a = -0.9c

Simplifying
a = -0.9c

Subproblem 3
Set the factor '(-9c + 10a)' equal to zero and attempt to solve:

Simplifying
-9c + 10a = 0

Reorder the terms:
10a + -9c = 0

Solving
10a + -9c = 0

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

Add '9c' to each side of the equation.
10a + -9c + 9c = 0 + 9c

Combine like terms: -9c + 9c = 0
10a + 0 = 0 + 9c
10a = 0 + 9c
Remove the zero:
10a = 9c

Divide each side by '10'.
a = 0.9c

Simplifying
a = 0.9c
Solution
a = {0, -0.9c, 0.9c}

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