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Simplifying 6x(4x + 2y + -2) + -3x = 0 Reorder the terms: 6x(-2 + 4x + 2y) + -3x = 0 (-2 * 6x + 4x * 6x + 2y * 6x) + -3x = 0 Reorder the terms: (-12x + 12xy + 24x2) + -3x = 0 (-12x + 12xy + 24x2) + -3x = 0 Reorder the terms: -12x + -3x + 12xy + 24x2 = 0 Combine like terms: -12x + -3x = -15x -15x + 12xy + 24x2 = 0 Solving -15x + 12xy + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-5 + 4y + 8x) = 0 Ignore the factor 3.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 = 0Subproblem 2
Set the factor '(-5 + 4y + 8x)' equal to zero and attempt to solve: Simplifying -5 + 4y + 8x = 0 Reorder the terms: -5 + 8x + 4y = 0 Solving -5 + 8x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 8x + 5 + 4y = 0 + 5 Reorder the terms: -5 + 5 + 8x + 4y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 8x + 4y = 0 + 5 8x + 4y = 0 + 5 Combine like terms: 0 + 5 = 5 8x + 4y = 5 Add '-4y' to each side of the equation. 8x + 4y + -4y = 5 + -4y Combine like terms: 4y + -4y = 0 8x + 0 = 5 + -4y 8x = 5 + -4y Divide each side by '8'. x = 0.625 + -0.5y Simplifying x = 0.625 + -0.5ySolution
x = {0, 0.625 + -0.5y}
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