(10a-3c^2)(2a-c^2)=

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Solution for (10a-3c^2)(2a-c^2)= equation: 


Simplifying
(10a + -3c2)(2a + -1c2) = 0

Multiply (10a + -3c2) * (2a + -1c2)
(10a * (2a + -1c2) + -3c2 * (2a + -1c2)) = 0
((2a * 10a + -1c2 * 10a) + -3c2 * (2a + -1c2)) = 0

Reorder the terms:
((-10ac2 + 20a2) + -3c2 * (2a + -1c2)) = 0
((-10ac2 + 20a2) + -3c2 * (2a + -1c2)) = 0
(-10ac2 + 20a2 + (2a * -3c2 + -1c2 * -3c2)) = 0
(-10ac2 + 20a2 + (-6ac2 + 3c4)) = 0

Reorder the terms:
(-10ac2 + -6ac2 + 20a2 + 3c4) = 0

Combine like terms: -10ac2 + -6ac2 = -16ac2
(-16ac2 + 20a2 + 3c4) = 0

Solving
-16ac2 + 20a2 + 3c4 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -1c2)(10a + -3c2) = 0


Subproblem 1
Set the factor '(2a + -1c2)' equal to zero and attempt to solve:

Simplifying
2a + -1c2 = 0

Solving
2a + -1c2 = 0

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

Add 'c2' to each side of the equation.
2a + -1c2 + c2 = 0 + c2

Combine like terms: -1c2 + c2 = 0
2a + 0 = 0 + c2
2a = 0 + c2
Remove the zero:
2a = c2

Divide each side by '2'.
a = 0.5c2

Simplifying
a = 0.5c2

Subproblem 2
Set the factor '(10a + -3c2)' equal to zero and attempt to solve:

Simplifying
10a + -3c2 = 0

Solving
10a + -3c2 = 0

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

Add '3c2' to each side of the equation.
10a + -3c2 + 3c2 = 0 + 3c2

Combine like terms: -3c2 + 3c2 = 0
10a + 0 = 0 + 3c2
10a = 0 + 3c2
Remove the zero:
10a = 3c2

Divide each side by '10'.
a = 0.3c2

Simplifying
a = 0.3c2
Solution
a = {0.5c2, 0.3c2}

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