(12a+3)*4-(9-7y)*5=8(3y-5)

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Solution for (12a+3)*4-(9-7y)*5=8(3y-5) equation: 


Simplifying
(12a + 3) * 4 + -1(9 + -7y) * 5 = 8(3y + -5)

Reorder the terms:
(3 + 12a) * 4 + -1(9 + -7y) * 5 = 8(3y + -5)

Reorder the terms for easier multiplication:
4(3 + 12a) + -1(9 + -7y) * 5 = 8(3y + -5)
(3 * 4 + 12a * 4) + -1(9 + -7y) * 5 = 8(3y + -5)
(12 + 48a) + -1(9 + -7y) * 5 = 8(3y + -5)

Reorder the terms for easier multiplication:
12 + 48a + -1 * 5(9 + -7y) = 8(3y + -5)

Multiply -1 * 5
12 + 48a + -5(9 + -7y) = 8(3y + -5)
12 + 48a + (9 * -5 + -7y * -5) = 8(3y + -5)
12 + 48a + (-45 + 35y) = 8(3y + -5)

Reorder the terms:
12 + -45 + 48a + 35y = 8(3y + -5)

Combine like terms: 12 + -45 = -33
-33 + 48a + 35y = 8(3y + -5)

Reorder the terms:
-33 + 48a + 35y = 8(-5 + 3y)
-33 + 48a + 35y = (-5 * 8 + 3y * 8)
-33 + 48a + 35y = (-40 + 24y)

Solving
-33 + 48a + 35y = -40 + 24y

Solving for variable 'a'.

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

Add '33' to each side of the equation.
-33 + 48a + 33 + 35y = -40 + 33 + 24y

Reorder the terms:
-33 + 33 + 48a + 35y = -40 + 33 + 24y

Combine like terms: -33 + 33 = 0
0 + 48a + 35y = -40 + 33 + 24y
48a + 35y = -40 + 33 + 24y

Combine like terms: -40 + 33 = -7
48a + 35y = -7 + 24y

Add '-35y' to each side of the equation.
48a + 35y + -35y = -7 + 24y + -35y

Combine like terms: 35y + -35y = 0
48a + 0 = -7 + 24y + -35y
48a = -7 + 24y + -35y

Combine like terms: 24y + -35y = -11y
48a = -7 + -11y

Divide each side by '48'.
a = -0.1458333333 + -0.2291666667y

Simplifying
a = -0.1458333333 + -0.2291666667y

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