-20y=4y^2+25

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Solution for -20y=4y^2+25 equation:


Simplifying
-20y = 4y2 + 25

Reorder the terms:
-20y = 25 + 4y2

Solving
-20y = 25 + 4y2

Solving for variable 'y'.

Reorder the terms:
-25 + -20y + -4y2 = 25 + 4y2 + -25 + -4y2

Reorder the terms:
-25 + -20y + -4y2 = 25 + -25 + 4y2 + -4y2

Combine like terms: 25 + -25 = 0
-25 + -20y + -4y2 = 0 + 4y2 + -4y2
-25 + -20y + -4y2 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
-25 + -20y + -4y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(25 + 20y + 4y2) = 0

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

Ignore the factor -1.

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 + 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

Solution

y = {-2.5, -2.5}

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