-3a(a+b-5)+4(-2a+2b)=b(a+3b-7)

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Solution for -3a(a+b-5)+4(-2a+2b)=b(a+3b-7) equation: 


Simplifying
-3a(a + b + -5) + 4(-2a + 2b) = b(a + 3b + -7)

Reorder the terms:
-3a(-5 + a + b) + 4(-2a + 2b) = b(a + 3b + -7)
(-5 * -3a + a * -3a + b * -3a) + 4(-2a + 2b) = b(a + 3b + -7)

Reorder the terms:
(15a + -3ab + -3a2) + 4(-2a + 2b) = b(a + 3b + -7)
(15a + -3ab + -3a2) + 4(-2a + 2b) = b(a + 3b + -7)
15a + -3ab + -3a2 + (-2a * 4 + 2b * 4) = b(a + 3b + -7)
15a + -3ab + -3a2 + (-8a + 8b) = b(a + 3b + -7)

Reorder the terms:
15a + -8a + -3ab + -3a2 + 8b = b(a + 3b + -7)

Combine like terms: 15a + -8a = 7a
7a + -3ab + -3a2 + 8b = b(a + 3b + -7)

Reorder the terms:
7a + -3ab + -3a2 + 8b = b(-7 + a + 3b)
7a + -3ab + -3a2 + 8b = (-7 * b + a * b + 3b * b)

Reorder the terms:
7a + -3ab + -3a2 + 8b = (ab + -7b + 3b2)
7a + -3ab + -3a2 + 8b = (ab + -7b + 3b2)

Solving
7a + -3ab + -3a2 + 8b = ab + -7b + 3b2

Solving for variable 'a'.

Reorder the terms:
7a + -3ab + -1ab + -3a2 + 8b + 7b + -3b2 = ab + -7b + 3b2 + -1ab + 7b + -3b2

Combine like terms: -3ab + -1ab = -4ab
7a + -4ab + -3a2 + 8b + 7b + -3b2 = ab + -7b + 3b2 + -1ab + 7b + -3b2

Combine like terms: 8b + 7b = 15b
7a + -4ab + -3a2 + 15b + -3b2 = ab + -7b + 3b2 + -1ab + 7b + -3b2

Reorder the terms:
7a + -4ab + -3a2 + 15b + -3b2 = ab + -1ab + -7b + 7b + 3b2 + -3b2

Combine like terms: ab + -1ab = 0
7a + -4ab + -3a2 + 15b + -3b2 = 0 + -7b + 7b + 3b2 + -3b2
7a + -4ab + -3a2 + 15b + -3b2 = -7b + 7b + 3b2 + -3b2

Combine like terms: -7b + 7b = 0
7a + -4ab + -3a2 + 15b + -3b2 = 0 + 3b2 + -3b2
7a + -4ab + -3a2 + 15b + -3b2 = 3b2 + -3b2

Combine like terms: 3b2 + -3b2 = 0
7a + -4ab + -3a2 + 15b + -3b2 = 0

The solution to this equation could not be determined.

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