(3y-1)(3y+1)=(4y-3)(2y+1)

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Solution for (3y-1)(3y+1)=(4y-3)(2y+1) equation: 


Simplifying
(3y + -1)(3y + 1) = (4y + -3)(2y + 1)

Reorder the terms:
(-1 + 3y)(3y + 1) = (4y + -3)(2y + 1)

Reorder the terms:
(-1 + 3y)(1 + 3y) = (4y + -3)(2y + 1)

Multiply (-1 + 3y) * (1 + 3y)
(-1(1 + 3y) + 3y * (1 + 3y)) = (4y + -3)(2y + 1)
((1 * -1 + 3y * -1) + 3y * (1 + 3y)) = (4y + -3)(2y + 1)
((-1 + -3y) + 3y * (1 + 3y)) = (4y + -3)(2y + 1)
(-1 + -3y + (1 * 3y + 3y * 3y)) = (4y + -3)(2y + 1)
(-1 + -3y + (3y + 9y2)) = (4y + -3)(2y + 1)

Combine like terms: -3y + 3y = 0
(-1 + 0 + 9y2) = (4y + -3)(2y + 1)
(-1 + 9y2) = (4y + -3)(2y + 1)

Reorder the terms:
-1 + 9y2 = (-3 + 4y)(2y + 1)

Reorder the terms:
-1 + 9y2 = (-3 + 4y)(1 + 2y)

Multiply (-3 + 4y) * (1 + 2y)
-1 + 9y2 = (-3(1 + 2y) + 4y * (1 + 2y))
-1 + 9y2 = ((1 * -3 + 2y * -3) + 4y * (1 + 2y))
-1 + 9y2 = ((-3 + -6y) + 4y * (1 + 2y))
-1 + 9y2 = (-3 + -6y + (1 * 4y + 2y * 4y))
-1 + 9y2 = (-3 + -6y + (4y + 8y2))

Combine like terms: -6y + 4y = -2y
-1 + 9y2 = (-3 + -2y + 8y2)

Solving
-1 + 9y2 = -3 + -2y + 8y2

Solving for variable 'y'.

Reorder the terms:
-1 + 3 + 2y + 9y2 + -8y2 = -3 + -2y + 8y2 + 3 + 2y + -8y2

Combine like terms: -1 + 3 = 2
2 + 2y + 9y2 + -8y2 = -3 + -2y + 8y2 + 3 + 2y + -8y2

Combine like terms: 9y2 + -8y2 = 1y2
2 + 2y + 1y2 = -3 + -2y + 8y2 + 3 + 2y + -8y2

Reorder the terms:
2 + 2y + 1y2 = -3 + 3 + -2y + 2y + 8y2 + -8y2

Combine like terms: -3 + 3 = 0
2 + 2y + 1y2 = 0 + -2y + 2y + 8y2 + -8y2
2 + 2y + 1y2 = -2y + 2y + 8y2 + -8y2

Combine like terms: -2y + 2y = 0
2 + 2y + 1y2 = 0 + 8y2 + -8y2
2 + 2y + 1y2 = 8y2 + -8y2

Combine like terms: 8y2 + -8y2 = 0
2 + 2y + 1y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + 2y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2y + y2 = 0 + -2
2y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
2y + y2 = -2

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = -2 + 1

Reorder the terms:
1 + 2y + y2 = -2 + 1

Combine like terms: -2 + 1 = -1
1 + 2y + y2 = -1

Factor a perfect square on the left side:
(y + 1)(y + 1) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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