(a-b)*(a+3b)-(a-3b)*(a-2b)=7a

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


Simplifying
(a + -1b)(a + 3b) + -1(a + -3b)(a + -2b) = 7a

Multiply (a + -1b) * (a + 3b)
(a(a + 3b) + -1b * (a + 3b)) + -1(a + -3b)(a + -2b) = 7a
((a * a + 3b * a) + -1b * (a + 3b)) + -1(a + -3b)(a + -2b) = 7a

Reorder the terms:
((3ab + a2) + -1b * (a + 3b)) + -1(a + -3b)(a + -2b) = 7a
((3ab + a2) + -1b * (a + 3b)) + -1(a + -3b)(a + -2b) = 7a
(3ab + a2 + (a * -1b + 3b * -1b)) + -1(a + -3b)(a + -2b) = 7a
(3ab + a2 + (-1ab + -3b2)) + -1(a + -3b)(a + -2b) = 7a

Reorder the terms:
(3ab + -1ab + a2 + -3b2) + -1(a + -3b)(a + -2b) = 7a

Combine like terms: 3ab + -1ab = 2ab
(2ab + a2 + -3b2) + -1(a + -3b)(a + -2b) = 7a

Multiply (a + -3b) * (a + -2b)
2ab + a2 + -3b2 + -1(a(a + -2b) + -3b * (a + -2b)) = 7a
2ab + a2 + -3b2 + -1((a * a + -2b * a) + -3b * (a + -2b)) = 7a

Reorder the terms:
2ab + a2 + -3b2 + -1((-2ab + a2) + -3b * (a + -2b)) = 7a
2ab + a2 + -3b2 + -1((-2ab + a2) + -3b * (a + -2b)) = 7a
2ab + a2 + -3b2 + -1(-2ab + a2 + (a * -3b + -2b * -3b)) = 7a
2ab + a2 + -3b2 + -1(-2ab + a2 + (-3ab + 6b2)) = 7a

Reorder the terms:
2ab + a2 + -3b2 + -1(-2ab + -3ab + a2 + 6b2) = 7a

Combine like terms: -2ab + -3ab = -5ab
2ab + a2 + -3b2 + -1(-5ab + a2 + 6b2) = 7a
2ab + a2 + -3b2 + (-5ab * -1 + a2 * -1 + 6b2 * -1) = 7a
2ab + a2 + -3b2 + (5ab + -1a2 + -6b2) = 7a

Reorder the terms:
2ab + 5ab + a2 + -1a2 + -3b2 + -6b2 = 7a

Combine like terms: 2ab + 5ab = 7ab
7ab + a2 + -1a2 + -3b2 + -6b2 = 7a

Combine like terms: a2 + -1a2 = 0
7ab + 0 + -3b2 + -6b2 = 7a
7ab + -3b2 + -6b2 = 7a

Combine like terms: -3b2 + -6b2 = -9b2
7ab + -9b2 = 7a

Solving
7ab + -9b2 = 7a

Solving for variable 'a'.

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

Add '-7a' to each side of the equation.
7ab + -7a + -9b2 = 7a + -7a

Reorder the terms:
-7a + 7ab + -9b2 = 7a + -7a

Combine like terms: 7a + -7a = 0
-7a + 7ab + -9b2 = 0

Add '9b2' to each side of the equation.
-7a + 7ab + -9b2 + 9b2 = 0 + 9b2

Combine like terms: -9b2 + 9b2 = 0
-7a + 7ab + 0 = 0 + 9b2
-7a + 7ab = 0 + 9b2
Remove the zero:
-7a + 7ab = 9b2

Combine like terms: 9b2 + -9b2 = 0
-7a + 7ab + -9b2 = 0

The solution to this equation could not be determined.

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