y(2y+3)=-2y(y-5)

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Solution for y(2y+3)=-2y(y-5) equation: 


Simplifying
y(2y + 3) = -2y(y + -5)

Reorder the terms:
y(3 + 2y) = -2y(y + -5)
(3 * y + 2y * y) = -2y(y + -5)
(3y + 2y2) = -2y(y + -5)

Reorder the terms:
3y + 2y2 = -2y(-5 + y)
3y + 2y2 = (-5 * -2y + y * -2y)
3y + 2y2 = (10y + -2y2)

Solving
3y + 2y2 = 10y + -2y2

Solving for variable 'y'.

Reorder the terms:
3y + -10y + 2y2 + 2y2 = 10y + -2y2 + -10y + 2y2

Combine like terms: 3y + -10y = -7y
-7y + 2y2 + 2y2 = 10y + -2y2 + -10y + 2y2

Combine like terms: 2y2 + 2y2 = 4y2
-7y + 4y2 = 10y + -2y2 + -10y + 2y2

Reorder the terms:
-7y + 4y2 = 10y + -10y + -2y2 + 2y2

Combine like terms: 10y + -10y = 0
-7y + 4y2 = 0 + -2y2 + 2y2
-7y + 4y2 = -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
-7y + 4y2 = 0

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


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(-7 + 4y)' equal to zero and attempt to solve:

Simplifying
-7 + 4y = 0

Solving
-7 + 4y = 0

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

Add '7' to each side of the equation.
-7 + 7 + 4y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4y = 0 + 7
4y = 0 + 7

Combine like terms: 0 + 7 = 7
4y = 7

Divide each side by '4'.
y = 1.75

Simplifying
y = 1.75
Solution
y = {0, 1.75}

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