Solve for y
y = -\frac{46}{17} = -2\frac{12}{17} \approx -2.705882353
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13\left(4y+5\right)=9\left(2y-3\right)
Variable y cannot be equal to \frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by 13\left(2y-3\right), the least common multiple of 2y-3,13.
52y+65=9\left(2y-3\right)
Use the distributive property to multiply 13 by 4y+5.
52y+65=18y-27
Use the distributive property to multiply 9 by 2y-3.
52y+65-18y=-27
Subtract 18y from both sides.
34y+65=-27
Combine 52y and -18y to get 34y.
34y=-27-65
Subtract 65 from both sides.
34y=-92
Subtract 65 from -27 to get -92.
y=\frac{-92}{34}
Divide both sides by 34.
y=-\frac{46}{17}
Reduce the fraction \frac{-92}{34} to lowest terms by extracting and canceling out 2.
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