(5-2a)*(b+8)=(6b-7)*(3-a)

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Solution for (5-2a)*(b+8)=(6b-7)*(3-a) equation: 


Simplifying
(5 + -2a)(b + 8) = (6b + -7)(3 + -1a)

Reorder the terms:
(5 + -2a)(8 + b) = (6b + -7)(3 + -1a)

Multiply (5 + -2a) * (8 + b)
(5(8 + b) + -2a * (8 + b)) = (6b + -7)(3 + -1a)
((8 * 5 + b * 5) + -2a * (8 + b)) = (6b + -7)(3 + -1a)
((40 + 5b) + -2a * (8 + b)) = (6b + -7)(3 + -1a)
(40 + 5b + (8 * -2a + b * -2a)) = (6b + -7)(3 + -1a)
(40 + 5b + (-16a + -2ab)) = (6b + -7)(3 + -1a)

Reorder the terms:
(40 + -16a + -2ab + 5b) = (6b + -7)(3 + -1a)
(40 + -16a + -2ab + 5b) = (6b + -7)(3 + -1a)

Reorder the terms:
40 + -16a + -2ab + 5b = (-7 + 6b)(3 + -1a)

Multiply (-7 + 6b) * (3 + -1a)
40 + -16a + -2ab + 5b = (-7(3 + -1a) + 6b * (3 + -1a))
40 + -16a + -2ab + 5b = ((3 * -7 + -1a * -7) + 6b * (3 + -1a))
40 + -16a + -2ab + 5b = ((-21 + 7a) + 6b * (3 + -1a))
40 + -16a + -2ab + 5b = (-21 + 7a + (3 * 6b + -1a * 6b))

Reorder the terms:
40 + -16a + -2ab + 5b = (-21 + 7a + (-6ab + 18b))
40 + -16a + -2ab + 5b = (-21 + 7a + (-6ab + 18b))
40 + -16a + -2ab + 5b = (-21 + 7a + -6ab + 18b)

Solving
40 + -16a + -2ab + 5b = -21 + 7a + -6ab + 18b

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.
40 + -16a + -2ab + -7a + 5b = -21 + 7a + -6ab + -7a + 18b

Reorder the terms:
40 + -16a + -7a + -2ab + 5b = -21 + 7a + -6ab + -7a + 18b

Combine like terms: -16a + -7a = -23a
40 + -23a + -2ab + 5b = -21 + 7a + -6ab + -7a + 18b

Reorder the terms:
40 + -23a + -2ab + 5b = -21 + 7a + -7a + -6ab + 18b

Combine like terms: 7a + -7a = 0
40 + -23a + -2ab + 5b = -21 + 0 + -6ab + 18b
40 + -23a + -2ab + 5b = -21 + -6ab + 18b

Add '6ab' to each side of the equation.
40 + -23a + -2ab + 6ab + 5b = -21 + -6ab + 6ab + 18b

Combine like terms: -2ab + 6ab = 4ab
40 + -23a + 4ab + 5b = -21 + -6ab + 6ab + 18b

Combine like terms: -6ab + 6ab = 0
40 + -23a + 4ab + 5b = -21 + 0 + 18b
40 + -23a + 4ab + 5b = -21 + 18b

Add '-40' to each side of the equation.
40 + -23a + 4ab + -40 + 5b = -21 + -40 + 18b

Reorder the terms:
40 + -40 + -23a + 4ab + 5b = -21 + -40 + 18b

Combine like terms: 40 + -40 = 0
0 + -23a + 4ab + 5b = -21 + -40 + 18b
-23a + 4ab + 5b = -21 + -40 + 18b

Combine like terms: -21 + -40 = -61
-23a + 4ab + 5b = -61 + 18b

Add '-5b' to each side of the equation.
-23a + 4ab + 5b + -5b = -61 + 18b + -5b

Combine like terms: 5b + -5b = 0
-23a + 4ab + 0 = -61 + 18b + -5b
-23a + 4ab = -61 + 18b + -5b

Combine like terms: 18b + -5b = 13b
-23a + 4ab = -61 + 13b

Reorder the terms:
61 + -23a + 4ab + -13b = -61 + 13b + 61 + -13b

Reorder the terms:
61 + -23a + 4ab + -13b = -61 + 61 + 13b + -13b

Combine like terms: -61 + 61 = 0
61 + -23a + 4ab + -13b = 0 + 13b + -13b
61 + -23a + 4ab + -13b = 13b + -13b

Combine like terms: 13b + -13b = 0
61 + -23a + 4ab + -13b = 0

The solution to this equation could not be determined.

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