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Simplifying 7y(y + 2v + -6) + 3v(y + 2v + -6) + -4(Y + 2v + -6) = 0 Reorder the terms: 7y(-6 + 2v + y) + 3v(y + 2v + -6) + -4(Y + 2v + -6) = 0 (-6 * 7y + 2v * 7y + y * 7y) + 3v(y + 2v + -6) + -4(Y + 2v + -6) = 0 Reorder the terms: (14vy + -42y + 7y2) + 3v(y + 2v + -6) + -4(Y + 2v + -6) = 0 (14vy + -42y + 7y2) + 3v(y + 2v + -6) + -4(Y + 2v + -6) = 0 Reorder the terms: 14vy + -42y + 7y2 + 3v(-6 + 2v + y) + -4(Y + 2v + -6) = 0 14vy + -42y + 7y2 + (-6 * 3v + 2v * 3v + y * 3v) + -4(Y + 2v + -6) = 0 Reorder the terms: 14vy + -42y + 7y2 + (-18v + 3vy + 6v2) + -4(Y + 2v + -6) = 0 14vy + -42y + 7y2 + (-18v + 3vy + 6v2) + -4(Y + 2v + -6) = 0 Reorder the terms: 14vy + -42y + 7y2 + -18v + 3vy + 6v2 + -4(-6 + Y + 2v) = 0 14vy + -42y + 7y2 + -18v + 3vy + 6v2 + (-6 * -4 + Y * -4 + 2v * -4) = 0 14vy + -42y + 7y2 + -18v + 3vy + 6v2 + (24 + -4Y + -8v) = 0 Reorder the terms: 24 + -4Y + -18v + -8v + 14vy + 3vy + 6v2 + -42y + 7y2 = 0 Combine like terms: -18v + -8v = -26v 24 + -4Y + -26v + 14vy + 3vy + 6v2 + -42y + 7y2 = 0 Combine like terms: 14vy + 3vy = 17vy 24 + -4Y + -26v + 17vy + 6v2 + -42y + 7y2 = 0 Solving 24 + -4Y + -26v + 17vy + 6v2 + -42y + 7y2 = 0 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -4Y + -26v + 17vy + 6v2 + -42y + -24 + 7y2 = 0 + -24 Reorder the terms: 24 + -24 + -4Y + -26v + 17vy + 6v2 + -42y + 7y2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -4Y + -26v + 17vy + 6v2 + -42y + 7y2 = 0 + -24 -4Y + -26v + 17vy + 6v2 + -42y + 7y2 = 0 + -24 Combine like terms: 0 + -24 = -24 -4Y + -26v + 17vy + 6v2 + -42y + 7y2 = -24 Add '26v' to each side of the equation. -4Y + -26v + 17vy + 6v2 + -42y + 26v + 7y2 = -24 + 26v Reorder the terms: -4Y + -26v + 26v + 17vy + 6v2 + -42y + 7y2 = -24 + 26v Combine like terms: -26v + 26v = 0 -4Y + 0 + 17vy + 6v2 + -42y + 7y2 = -24 + 26v -4Y + 17vy + 6v2 + -42y + 7y2 = -24 + 26v Add '-17vy' to each side of the equation. -4Y + 17vy + 6v2 + -42y + -17vy + 7y2 = -24 + 26v + -17vy Reorder the terms: -4Y + 17vy + -17vy + 6v2 + -42y + 7y2 = -24 + 26v + -17vy Combine like terms: 17vy + -17vy = 0 -4Y + 0 + 6v2 + -42y + 7y2 = -24 + 26v + -17vy -4Y + 6v2 + -42y + 7y2 = -24 + 26v + -17vy Add '-6v2' to each side of the equation. -4Y + 6v2 + -42y + -6v2 + 7y2 = -24 + 26v + -17vy + -6v2 Reorder the terms: -4Y + 6v2 + -6v2 + -42y + 7y2 = -24 + 26v + -17vy + -6v2 Combine like terms: 6v2 + -6v2 = 0 -4Y + 0 + -42y + 7y2 = -24 + 26v + -17vy + -6v2 -4Y + -42y + 7y2 = -24 + 26v + -17vy + -6v2 Add '42y' to each side of the equation. -4Y + -42y + 42y + 7y2 = -24 + 26v + -17vy + -6v2 + 42y Combine like terms: -42y + 42y = 0 -4Y + 0 + 7y2 = -24 + 26v + -17vy + -6v2 + 42y -4Y + 7y2 = -24 + 26v + -17vy + -6v2 + 42y Add '-7y2' to each side of the equation. -4Y + 7y2 + -7y2 = -24 + 26v + -17vy + -6v2 + 42y + -7y2 Combine like terms: 7y2 + -7y2 = 0 -4Y + 0 = -24 + 26v + -17vy + -6v2 + 42y + -7y2 -4Y = -24 + 26v + -17vy + -6v2 + 42y + -7y2 Divide each side by '-4'. Y = 6 + -6.5v + 4.25vy + 1.5v2 + -10.5y + 1.75y2 Simplifying Y = 6 + -6.5v + 4.25vy + 1.5v2 + -10.5y + 1.75y2
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