4y(4y+1)+(4y+1)=0

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Solution for 4y(4y+1)+(4y+1)=0 equation:


Simplifying
4y(4y + 1) + (4y + 1) = 0

Reorder the terms:
4y(1 + 4y) + (4y + 1) = 0
(1 * 4y + 4y * 4y) + (4y + 1) = 0
(4y + 16y2) + (4y + 1) = 0

Reorder the terms:
4y + 16y2 + (1 + 4y) = 0

Remove parenthesis around (1 + 4y)
4y + 16y2 + 1 + 4y = 0

Reorder the terms:
1 + 4y + 4y + 16y2 = 0

Combine like terms: 4y + 4y = 8y
1 + 8y + 16y2 = 0

Solving
1 + 8y + 16y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(1 + 4y)(1 + 4y) = 0

Subproblem 1

Set the factor '(1 + 4y)' equal to zero and attempt to solve: Simplifying 1 + 4y = 0 Solving 1 + 4y = 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 + 4y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4y = 0 + -1 4y = 0 + -1 Combine like terms: 0 + -1 = -1 4y = -1 Divide each side by '4'. y = -0.25 Simplifying y = -0.25

Subproblem 2

Set the factor '(1 + 4y)' equal to zero and attempt to solve: Simplifying 1 + 4y = 0 Solving 1 + 4y = 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 + 4y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4y = 0 + -1 4y = 0 + -1 Combine like terms: 0 + -1 = -1 4y = -1 Divide each side by '4'. y = -0.25 Simplifying y = -0.25

Solution

y = {-0.25, -0.25}

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