(8y+4)(5y+10)=0

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Solution for (8y+4)(5y+10)=0 equation:


Simplifying
(8y + 4)(5y + 10) = 0

Reorder the terms:
(4 + 8y)(5y + 10) = 0

Reorder the terms:
(4 + 8y)(10 + 5y) = 0

Multiply (4 + 8y) * (10 + 5y)
(4(10 + 5y) + 8y * (10 + 5y)) = 0
((10 * 4 + 5y * 4) + 8y * (10 + 5y)) = 0
((40 + 20y) + 8y * (10 + 5y)) = 0
(40 + 20y + (10 * 8y + 5y * 8y)) = 0
(40 + 20y + (80y + 40y2)) = 0

Combine like terms: 20y + 80y = 100y
(40 + 100y + 40y2) = 0

Solving
40 + 100y + 40y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '20'.
20(2 + 5y + 2y2) = 0

Factor a trinomial.
20((2 + y)(1 + 2y)) = 0

Ignore the factor 20.

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 '(1 + 2y)' equal to zero and attempt to solve: Simplifying 1 + 2y = 0 Solving 1 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2y = 0 + -1 2y = 0 + -1 Combine like terms: 0 + -1 = -1 2y = -1 Divide each side by '2'. y = -0.5 Simplifying y = -0.5

Solution

y = {-2, -0.5}

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