(3y-7)*(9+4y)=(6y-1)*(5+2y)

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Solution for (3y-7)*(9+4y)=(6y-1)*(5+2y) equation: 


Simplifying
(3y + -7)(9 + 4y) = (6y + -1)(5 + 2y)

Reorder the terms:
(-7 + 3y)(9 + 4y) = (6y + -1)(5 + 2y)

Multiply (-7 + 3y) * (9 + 4y)
(-7(9 + 4y) + 3y * (9 + 4y)) = (6y + -1)(5 + 2y)
((9 * -7 + 4y * -7) + 3y * (9 + 4y)) = (6y + -1)(5 + 2y)
((-63 + -28y) + 3y * (9 + 4y)) = (6y + -1)(5 + 2y)
(-63 + -28y + (9 * 3y + 4y * 3y)) = (6y + -1)(5 + 2y)
(-63 + -28y + (27y + 12y2)) = (6y + -1)(5 + 2y)

Combine like terms: -28y + 27y = -1y
(-63 + -1y + 12y2) = (6y + -1)(5 + 2y)

Reorder the terms:
-63 + -1y + 12y2 = (-1 + 6y)(5 + 2y)

Multiply (-1 + 6y) * (5 + 2y)
-63 + -1y + 12y2 = (-1(5 + 2y) + 6y * (5 + 2y))
-63 + -1y + 12y2 = ((5 * -1 + 2y * -1) + 6y * (5 + 2y))
-63 + -1y + 12y2 = ((-5 + -2y) + 6y * (5 + 2y))
-63 + -1y + 12y2 = (-5 + -2y + (5 * 6y + 2y * 6y))
-63 + -1y + 12y2 = (-5 + -2y + (30y + 12y2))

Combine like terms: -2y + 30y = 28y
-63 + -1y + 12y2 = (-5 + 28y + 12y2)

Add '-12y2' to each side of the equation.
-63 + -1y + 12y2 + -12y2 = -5 + 28y + 12y2 + -12y2

Combine like terms: 12y2 + -12y2 = 0
-63 + -1y + 0 = -5 + 28y + 12y2 + -12y2
-63 + -1y = -5 + 28y + 12y2 + -12y2

Combine like terms: 12y2 + -12y2 = 0
-63 + -1y = -5 + 28y + 0
-63 + -1y = -5 + 28y

Solving
-63 + -1y = -5 + 28y

Solving for variable 'y'.

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

Add '-28y' to each side of the equation.
-63 + -1y + -28y = -5 + 28y + -28y

Combine like terms: -1y + -28y = -29y
-63 + -29y = -5 + 28y + -28y

Combine like terms: 28y + -28y = 0
-63 + -29y = -5 + 0
-63 + -29y = -5

Add '63' to each side of the equation.
-63 + 63 + -29y = -5 + 63

Combine like terms: -63 + 63 = 0
0 + -29y = -5 + 63
-29y = -5 + 63

Combine like terms: -5 + 63 = 58
-29y = 58

Divide each side by '-29'.
y = -2

Simplifying
y = -2

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