(4y+8)(3y+2)=0

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Solution for (4y+8)(3y+2)=0 equation: 


Simplifying
(4y + 8)(3y + 2) = 0

Reorder the terms:
(8 + 4y)(3y + 2) = 0

Reorder the terms:
(8 + 4y)(2 + 3y) = 0

Multiply (8 + 4y) * (2 + 3y)
(8(2 + 3y) + 4y * (2 + 3y)) = 0
((2 * 8 + 3y * 8) + 4y * (2 + 3y)) = 0
((16 + 24y) + 4y * (2 + 3y)) = 0
(16 + 24y + (2 * 4y + 3y * 4y)) = 0
(16 + 24y + (8y + 12y2)) = 0

Combine like terms: 24y + 8y = 32y
(16 + 32y + 12y2) = 0

Solving
16 + 32y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + 8y + 3y2) = 0

Factor a trinomial.
4((2 + y)(2 + 3y)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

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

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

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

Simplifying
y = -2

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

Simplifying
2 + 3y = 0

Solving
2 + 3y = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3y = 0 + -2
3y = 0 + -2

Combine like terms: 0 + -2 = -2
3y = -2

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Solution
y = {-2, -0.6666666667}

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