(4y+8)(5y-3)=0

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Solution for (4y+8)(5y-3)=0 equation: 


Simplifying
(4y + 8)(5y + -3) = 0

Reorder the terms:
(8 + 4y)(5y + -3) = 0

Reorder the terms:
(8 + 4y)(-3 + 5y) = 0

Multiply (8 + 4y) * (-3 + 5y)
(8(-3 + 5y) + 4y * (-3 + 5y)) = 0
((-3 * 8 + 5y * 8) + 4y * (-3 + 5y)) = 0
((-24 + 40y) + 4y * (-3 + 5y)) = 0
(-24 + 40y + (-3 * 4y + 5y * 4y)) = 0
(-24 + 40y + (-12y + 20y2)) = 0

Combine like terms: 40y + -12y = 28y
(-24 + 28y + 20y2) = 0

Solving
-24 + 28y + 20y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 7y + 5y2) = 0

Factor a trinomial.
4((-2 + -1y)(3 + -5y)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2

Subproblem 2
Set the factor '(3 + -5y)' equal to zero and attempt to solve:

Simplifying
3 + -5y = 0

Solving
3 + -5y = 0

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

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

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

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

Divide each side by '-5'.
y = 0.6

Simplifying
y = 0.6
Solution
y = {-2, 0.6}

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