y(2y-4)=10-y(2y+4)

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Solution for y(2y-4)=10-y(2y+4) equation: 


Simplifying
y(2y + -4) = 10 + -1y(2y + 4)

Reorder the terms:
y(-4 + 2y) = 10 + -1y(2y + 4)
(-4 * y + 2y * y) = 10 + -1y(2y + 4)
(-4y + 2y2) = 10 + -1y(2y + 4)

Reorder the terms:
-4y + 2y2 = 10 + -1y(4 + 2y)
-4y + 2y2 = 10 + (4 * -1y + 2y * -1y)
-4y + 2y2 = 10 + (-4y + -2y2)

Add '4y' to each side of the equation.
-4y + 4y + 2y2 = 10 + -4y + 4y + -2y2

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

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

Solving
2y2 = 10 + -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.
2y2 + 2y2 = 10 + -2y2 + 2y2

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

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

Divide each side by '4'.
y2 = 2.5

Simplifying
y2 = 2.5

Take the square root of each side:
y = {-1.58113883, 1.58113883}

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