x(6x+5y^2-(4y-9)(4y))=0

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Solution for x(6x+5y^2-(4y-9)(4y))=0 equation:


Simplifying
x(6x + 5y2 + -1(4y + -9)(4y)) = 0

Reorder the terms:
x(6x + 5y2 + -1(-9 + 4y)(4y)) = 0

Remove parenthesis around (4y)
x(6x + 5y2 + -1(-9 + 4y) * 4y) = 0

Reorder the terms for easier multiplication:
x(6x + 5y2 + -1 * 4y(-9 + 4y)) = 0

Multiply -1 * 4
x(6x + 5y2 + -4y(-9 + 4y)) = 0
x(6x + 5y2 + (-9 * -4y + 4y * -4y)) = 0
x(6x + 5y2 + (36y + -16y2)) = 0

Reorder the terms:
x(6x + 36y + 5y2 + -16y2) = 0

Combine like terms: 5y2 + -16y2 = -11y2
x(6x + 36y + -11y2) = 0
(6x * x + 36y * x + -11y2 * x) = 0

Reorder the terms:
(36xy + -11xy2 + 6x2) = 0
(36xy + -11xy2 + 6x2) = 0

Solving
36xy + -11xy2 + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(36y + -11y2 + 6x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(36y + -11y2 + 6x)' equal to zero and attempt to solve: Simplifying 36y + -11y2 + 6x = 0 Reorder the terms: 6x + 36y + -11y2 = 0 Solving 6x + 36y + -11y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-36y' to each side of the equation. 6x + 36y + -36y + -11y2 = 0 + -36y Combine like terms: 36y + -36y = 0 6x + 0 + -11y2 = 0 + -36y 6x + -11y2 = 0 + -36y Remove the zero: 6x + -11y2 = -36y Add '11y2' to each side of the equation. 6x + -11y2 + 11y2 = -36y + 11y2 Combine like terms: -11y2 + 11y2 = 0 6x + 0 = -36y + 11y2 6x = -36y + 11y2 Divide each side by '6'. x = -6y + 1.833333333y2 Simplifying x = -6y + 1.833333333y2

Solution

x = {0, -6y + 1.833333333y2}

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