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

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


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

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

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

Multiply (-5 + 2y) * (7 + 3y)
(-5(7 + 3y) + 2y * (7 + 3y)) = 0
((7 * -5 + 3y * -5) + 2y * (7 + 3y)) = 0
((-35 + -15y) + 2y * (7 + 3y)) = 0
(-35 + -15y + (7 * 2y + 3y * 2y)) = 0
(-35 + -15y + (14y + 6y2)) = 0

Combine like terms: -15y + 14y = -1y
(-35 + -1y + 6y2) = 0

Solving
-35 + -1y + 6y2 = 0

Solving for variable 'y'.

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


Subproblem 1
Set the factor '(-7 + -3y)' equal to zero and attempt to solve:

Simplifying
-7 + -3y = 0

Solving
-7 + -3y = 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 + -3y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3y = 0 + 7
-3y = 0 + 7

Combine like terms: 0 + 7 = 7
-3y = 7

Divide each side by '-3'.
y = -2.333333333

Simplifying
y = -2.333333333

Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 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 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {-2.333333333, 2.5}

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