(3y+8)(2y+7)=0

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Solution for (3y+8)(2y+7)=0 equation: 


Simplifying
(3y + 8)(2y + 7) = 0

Reorder the terms:
(8 + 3y)(2y + 7) = 0

Reorder the terms:
(8 + 3y)(7 + 2y) = 0

Multiply (8 + 3y) * (7 + 2y)
(8(7 + 2y) + 3y * (7 + 2y)) = 0
((7 * 8 + 2y * 8) + 3y * (7 + 2y)) = 0
((56 + 16y) + 3y * (7 + 2y)) = 0
(56 + 16y + (7 * 3y + 2y * 3y)) = 0
(56 + 16y + (21y + 6y2)) = 0

Combine like terms: 16y + 21y = 37y
(56 + 37y + 6y2) = 0

Solving
56 + 37y + 6y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(7 + 2y)(8 + 3y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(8 + 3y)' equal to zero and attempt to solve:

Simplifying
8 + 3y = 0

Solving
8 + 3y = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3y = 0 + -8
3y = 0 + -8

Combine like terms: 0 + -8 = -8
3y = -8

Divide each side by '3'.
y = -2.666666667

Simplifying
y = -2.666666667
Solution
y = {-3.5, -2.666666667}

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