(2y+5)(7y+5)=0

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Solution for (2y+5)(7y+5)=0 equation:


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

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

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

Multiply (5 + 2y) * (5 + 7y)
(5(5 + 7y) + 2y * (5 + 7y)) = 0
((5 * 5 + 7y * 5) + 2y * (5 + 7y)) = 0
((25 + 35y) + 2y * (5 + 7y)) = 0
(25 + 35y + (5 * 2y + 7y * 2y)) = 0
(25 + 35y + (10y + 14y2)) = 0

Combine like terms: 35y + 10y = 45y
(25 + 45y + 14y2) = 0

Solving
25 + 45y + 14y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + 2y)(5 + 7y) = 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 '(5 + 7y)' equal to zero and attempt to solve: Simplifying 5 + 7y = 0 Solving 5 + 7y = 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 + 7y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7y = 0 + -5 7y = 0 + -5 Combine like terms: 0 + -5 = -5 7y = -5 Divide each side by '7'. y = -0.7142857143 Simplifying y = -0.7142857143

Solution

y = {-2.5, -0.7142857143}

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