(8a+2b)(-7a+3b)=0

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Solution for (8a+2b)(-7a+3b)=0 equation: 


Simplifying
(8a + 2b)(-7a + 3b) = 0

Multiply (8a + 2b) * (-7a + 3b)
(8a * (-7a + 3b) + 2b * (-7a + 3b)) = 0
((-7a * 8a + 3b * 8a) + 2b * (-7a + 3b)) = 0

Reorder the terms:
((24ab + -56a2) + 2b * (-7a + 3b)) = 0
((24ab + -56a2) + 2b * (-7a + 3b)) = 0
(24ab + -56a2 + (-7a * 2b + 3b * 2b)) = 0
(24ab + -56a2 + (-14ab + 6b2)) = 0

Reorder the terms:
(24ab + -14ab + -56a2 + 6b2) = 0

Combine like terms: 24ab + -14ab = 10ab
(10ab + -56a2 + 6b2) = 0

Solving
10ab + -56a2 + 6b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5ab + -28a2 + 3b2) = 0

Factor a trinomial.
2((-4a + -1b)(7a + -3b)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4a + -1b)' equal to zero and attempt to solve:

Simplifying
-4a + -1b = 0

Solving
-4a + -1b = 0

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

Add 'b' to each side of the equation.
-4a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
-4a + 0 = 0 + b
-4a = 0 + b
Remove the zero:
-4a = b

Divide each side by '-4'.
a = -0.25b

Simplifying
a = -0.25b

Subproblem 2
Set the factor '(7a + -3b)' equal to zero and attempt to solve:

Simplifying
7a + -3b = 0

Solving
7a + -3b = 0

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

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

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

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

Simplifying
a = 0.4285714286b
Solution
a = {-0.25b, 0.4285714286b}

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