3y(y-2)=y(2y-6)+16

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Solution for 3y(y-2)=y(2y-6)+16 equation:


Simplifying
3y(y + -2) = y(2y + -6) + 16

Reorder the terms:
3y(-2 + y) = y(2y + -6) + 16
(-2 * 3y + y * 3y) = y(2y + -6) + 16
(-6y + 3y2) = y(2y + -6) + 16

Reorder the terms:
-6y + 3y2 = y(-6 + 2y) + 16
-6y + 3y2 = (-6 * y + 2y * y) + 16
-6y + 3y2 = (-6y + 2y2) + 16

Reorder the terms:
-6y + 3y2 = 16 + -6y + 2y2

Add '6y' to each side of the equation.
-6y + 6y + 3y2 = 16 + -6y + 6y + 2y2

Combine like terms: -6y + 6y = 0
0 + 3y2 = 16 + -6y + 6y + 2y2
3y2 = 16 + -6y + 6y + 2y2

Combine like terms: -6y + 6y = 0
3y2 = 16 + 0 + 2y2
3y2 = 16 + 2y2

Solving
3y2 = 16 + 2y2

Solving for variable 'y'.

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

Add '-2y2' to each side of the equation.
3y2 + -2y2 = 16 + 2y2 + -2y2

Combine like terms: 3y2 + -2y2 = 1y2
1y2 = 16 + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
1y2 = 16 + 0
1y2 = 16

Divide each side by '1'.
y2 = 16

Simplifying
y2 = 16

Take the square root of each side:
y = {-4, 4}

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