(2a-6b)(7a-3b)=

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Solution for (2a-6b)(7a-3b)= equation: 


Simplifying
(2a + -6b)(7a + -3b) = 0

Multiply (2a + -6b) * (7a + -3b)
(2a * (7a + -3b) + -6b * (7a + -3b)) = 0
((7a * 2a + -3b * 2a) + -6b * (7a + -3b)) = 0

Reorder the terms:
((-6ab + 14a2) + -6b * (7a + -3b)) = 0
((-6ab + 14a2) + -6b * (7a + -3b)) = 0
(-6ab + 14a2 + (7a * -6b + -3b * -6b)) = 0
(-6ab + 14a2 + (-42ab + 18b2)) = 0

Reorder the terms:
(-6ab + -42ab + 14a2 + 18b2) = 0

Combine like terms: -6ab + -42ab = -48ab
(-48ab + 14a2 + 18b2) = 0

Solving
-48ab + 14a2 + 18b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24ab + 7a2 + 9b2) = 0

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

Ignore the factor 2.

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

Simplifying
a + -3b = 0

Solving
a + -3b = 0

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

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

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

Simplifying
a = 3b

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 = {3b, 0.4285714286b}

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