(7a-3c)(2a+c)=

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Solution for (7a-3c)(2a+c)= equation: 


Simplifying
(7a + -3c)(2a + c) = 0

Multiply (7a + -3c) * (2a + c)
(7a * (2a + c) + -3c * (2a + c)) = 0
((2a * 7a + c * 7a) + -3c * (2a + c)) = 0

Reorder the terms:
((7ac + 14a2) + -3c * (2a + c)) = 0
((7ac + 14a2) + -3c * (2a + c)) = 0
(7ac + 14a2 + (2a * -3c + c * -3c)) = 0
(7ac + 14a2 + (-6ac + -3c2)) = 0

Reorder the terms:
(7ac + -6ac + 14a2 + -3c2) = 0

Combine like terms: 7ac + -6ac = 1ac
(1ac + 14a2 + -3c2) = 0

Solving
1ac + 14a2 + -3c2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7a + -3c)(2a + c) = 0


Subproblem 1
Set the factor '(7a + -3c)' equal to zero and attempt to solve:

Simplifying
7a + -3c = 0

Solving
7a + -3c = 0

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

Add '3c' to each side of the equation.
7a + -3c + 3c = 0 + 3c

Combine like terms: -3c + 3c = 0
7a + 0 = 0 + 3c
7a = 0 + 3c
Remove the zero:
7a = 3c

Divide each side by '7'.
a = 0.4285714286c

Simplifying
a = 0.4285714286c

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

Simplifying
2a + c = 0

Solving
2a + c = 0

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

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

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

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

Simplifying
a = -0.5c
Solution
a = {0.4285714286c, -0.5c}

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