7a(a+b)-b(ab+a)=

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Solution for 7a(a+b)-b(ab+a)= equation: 


Simplifying
7a(a + b) + -1b(ab + a) = 0
(a * 7a + b * 7a) + -1b(ab + a) = 0

Reorder the terms:
(7ab + 7a2) + -1b(ab + a) = 0
(7ab + 7a2) + -1b(ab + a) = 0

Reorder the terms:
7ab + 7a2 + -1b(a + ab) = 0
7ab + 7a2 + (a * -1b + ab * -1b) = 0
7ab + 7a2 + (-1ab + -1ab2) = 0

Reorder the terms:
7ab + -1ab + -1ab2 + 7a2 = 0

Combine like terms: 7ab + -1ab = 6ab
6ab + -1ab2 + 7a2 = 0

Solving
6ab + -1ab2 + 7a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(6b + -1b2 + 7a) = 0


Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(6b + -1b2 + 7a)' equal to zero and attempt to solve:

Simplifying
6b + -1b2 + 7a = 0

Reorder the terms:
7a + 6b + -1b2 = 0

Solving
7a + 6b + -1b2 = 0

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

Add '-6b' to each side of the equation.
7a + 6b + -6b + -1b2 = 0 + -6b

Combine like terms: 6b + -6b = 0
7a + 0 + -1b2 = 0 + -6b
7a + -1b2 = 0 + -6b
Remove the zero:
7a + -1b2 = -6b

Add 'b2' to each side of the equation.
7a + -1b2 + b2 = -6b + b2

Combine like terms: -1b2 + b2 = 0
7a + 0 = -6b + b2
7a = -6b + b2

Divide each side by '7'.
a = -0.8571428571b + 0.1428571429b2

Simplifying
a = -0.8571428571b + 0.1428571429b2
Solution
a = {0, -0.8571428571b + 0.1428571429b2}

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