(3a+4c)(2a-3c)=

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Solution for (3a+4c)(2a-3c)= equation: 


Simplifying
(3a + 4c)(2a + -3c) = 0

Multiply (3a + 4c) * (2a + -3c)
(3a * (2a + -3c) + 4c * (2a + -3c)) = 0
((2a * 3a + -3c * 3a) + 4c * (2a + -3c)) = 0

Reorder the terms:
((-9ac + 6a2) + 4c * (2a + -3c)) = 0
((-9ac + 6a2) + 4c * (2a + -3c)) = 0
(-9ac + 6a2 + (2a * 4c + -3c * 4c)) = 0
(-9ac + 6a2 + (8ac + -12c2)) = 0

Reorder the terms:
(-9ac + 8ac + 6a2 + -12c2) = 0

Combine like terms: -9ac + 8ac = -1ac
(-1ac + 6a2 + -12c2) = 0

Solving
-1ac + 6a2 + -12c2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -3c)(3a + 4c) = 0


Subproblem 1
Set the factor '(2a + -3c)' equal to zero and attempt to solve:

Simplifying
2a + -3c = 0

Solving
2a + -3c = 0

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

Add '3c' to each side of the equation.
2a + -3c + 3c = 0 + 3c

Combine like terms: -3c + 3c = 0
2a + 0 = 0 + 3c
2a = 0 + 3c
Remove the zero:
2a = 3c

Divide each side by '2'.
a = 1.5c

Simplifying
a = 1.5c

Subproblem 2
Set the factor '(3a + 4c)' equal to zero and attempt to solve:

Simplifying
3a + 4c = 0

Solving
3a + 4c = 0

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

Add '-4c' to each side of the equation.
3a + 4c + -4c = 0 + -4c

Combine like terms: 4c + -4c = 0
3a + 0 = 0 + -4c
3a = 0 + -4c
Remove the zero:
3a = -4c

Divide each side by '3'.
a = -1.333333333c

Simplifying
a = -1.333333333c
Solution
a = {1.5c, -1.333333333c}

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