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

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


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

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

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

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

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

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

Solving for variable 'y'.

Combine like terms: 0 + 35 = 35
35 + y + -6y2 = -35 + -1y + 6y2 + 35 + y + -6y2

Reorder the terms:
35 + y + -6y2 = -35 + 35 + -1y + y + 6y2 + -6y2

Combine like terms: -35 + 35 = 0
35 + y + -6y2 = 0 + -1y + y + 6y2 + -6y2
35 + y + -6y2 = -1y + y + 6y2 + -6y2

Combine like terms: -1y + y = 0
35 + y + -6y2 = 0 + 6y2 + -6y2
35 + y + -6y2 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
35 + y + -6y2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
y = {2.5, -2.333333333}

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