(3y-5)(2y-7)=0

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Solution for (3y-5)(2y-7)=0 equation: 


Simplifying
(3y + -5)(2y + -7) = 0

Reorder the terms:
(-5 + 3y)(2y + -7) = 0

Reorder the terms:
(-5 + 3y)(-7 + 2y) = 0

Multiply (-5 + 3y) * (-7 + 2y)
(-5(-7 + 2y) + 3y * (-7 + 2y)) = 0
((-7 * -5 + 2y * -5) + 3y * (-7 + 2y)) = 0
((35 + -10y) + 3y * (-7 + 2y)) = 0
(35 + -10y + (-7 * 3y + 2y * 3y)) = 0
(35 + -10y + (-21y + 6y2)) = 0

Combine like terms: -10y + -21y = -31y
(35 + -31y + 6y2) = 0

Solving
35 + -31y + 6y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + -3y)(7 + -2y) = 0


Subproblem 1
Set the factor '(5 + -3y)' equal to zero and attempt to solve:

Simplifying
5 + -3y = 0

Solving
5 + -3y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3y = 0 + -5
-3y = 0 + -5

Combine like terms: 0 + -5 = -5
-3y = -5

Divide each side by '-3'.
y = 1.666666667

Simplifying
y = 1.666666667

Subproblem 2
Set the factor '(7 + -2y)' equal to zero and attempt to solve:

Simplifying
7 + -2y = 0

Solving
7 + -2y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {1.666666667, 3.5}

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