X^2-6y+8y^2=0

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Solution for X^2-6y+8y^2=0 equation:


Simplifying
X2 + -6y + 8y2 = 0

Solving
X2 + -6y + 8y2 = 0

Solving for variable 'X'.

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

Add '6y' to each side of the equation.
X2 + -6y + 6y + 8y2 = 0 + 6y

Combine like terms: -6y + 6y = 0
X2 + 0 + 8y2 = 0 + 6y
X2 + 8y2 = 0 + 6y
Remove the zero:
X2 + 8y2 = 6y

Add '-8y2' to each side of the equation.
X2 + 8y2 + -8y2 = 6y + -8y2

Combine like terms: 8y2 + -8y2 = 0
X2 + 0 = 6y + -8y2
X2 = 6y + -8y2

Simplifying
X2 = 6y + -8y2

Reorder the terms:
X2 + -6y + 8y2 = 6y + -6y + -8y2 + 8y2

Combine like terms: 6y + -6y = 0
X2 + -6y + 8y2 = 0 + -8y2 + 8y2
X2 + -6y + 8y2 = -8y2 + 8y2

Combine like terms: -8y2 + 8y2 = 0
X2 + -6y + 8y2 = 0

Factor a trinomial.
(X + -4y)(X + -2y) = 0

Subproblem 1

Set the factor '(X + -4y)' equal to zero and attempt to solve: Simplifying X + -4y = 0 Solving X + -4y = 0 Move all terms containing X to the left, all other terms to the right. Add '4y' to each side of the equation. X + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 X + 0 = 0 + 4y X = 0 + 4y Remove the zero: X = 4y Simplifying X = 4y

Subproblem 2

Set the factor '(X + -2y)' equal to zero and attempt to solve: Simplifying X + -2y = 0 Solving X + -2y = 0 Move all terms containing X to the left, all other terms to the right. Add '2y' to each side of the equation. X + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 X + 0 = 0 + 2y X = 0 + 2y Remove the zero: X = 2y Simplifying X = 2y

Solution

X = {4y, 2y}

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