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Simplifying 42x4 + -99x3y + -15x2y2 = 0 Reorder the terms: -15x2y2 + -99x3y + 42x4 = 0 Solving -15x2y2 + -99x3y + 42x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(-5y2 + -33xy + 14x2) = 0 Factor a trinomial. 3x2((-1y + -7x)(5y + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-1y + -7x)' equal to zero and attempt to solve: Simplifying -1y + -7x = 0 Reorder the terms: -7x + -1y = 0 Solving -7x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. -7x + -1y + y = 0 + y Combine like terms: -1y + y = 0 -7x + 0 = 0 + y -7x = 0 + y Remove the zero: -7x = y Divide each side by '-7'. x = -0.1428571429y Simplifying x = -0.1428571429ySubproblem 3
Set the factor '(5y + -2x)' equal to zero and attempt to solve: Simplifying 5y + -2x = 0 Reorder the terms: -2x + 5y = 0 Solving -2x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. -2x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 -2x + 0 = 0 + -5y -2x = 0 + -5y Remove the zero: -2x = -5y Divide each side by '-2'. x = 2.5y Simplifying x = 2.5ySolution
x = {0, -0.1428571429y, 2.5y}
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