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Simplifying (3x + 4)(5y + -2) = (5y + -2)(3 + 4) Reorder the terms: (4 + 3x)(5y + -2) = (5y + -2)(3 + 4) Reorder the terms: (4 + 3x)(-2 + 5y) = (5y + -2)(3 + 4) Multiply (4 + 3x) * (-2 + 5y) (4(-2 + 5y) + 3x * (-2 + 5y)) = (5y + -2)(3 + 4) ((-2 * 4 + 5y * 4) + 3x * (-2 + 5y)) = (5y + -2)(3 + 4) ((-8 + 20y) + 3x * (-2 + 5y)) = (5y + -2)(3 + 4) (-8 + 20y + (-2 * 3x + 5y * 3x)) = (5y + -2)(3 + 4) (-8 + 20y + (-6x + 15xy)) = (5y + -2)(3 + 4) Reorder the terms: (-8 + -6x + 15xy + 20y) = (5y + -2)(3 + 4) (-8 + -6x + 15xy + 20y) = (5y + -2)(3 + 4) Reorder the terms: -8 + -6x + 15xy + 20y = (-2 + 5y)(3 + 4) Combine like terms: 3 + 4 = 7 -8 + -6x + 15xy + 20y = (-2 + 5y)(7) Reorder the terms for easier multiplication: -8 + -6x + 15xy + 20y = 7(-2 + 5y) -8 + -6x + 15xy + 20y = (-2 * 7 + 5y * 7) -8 + -6x + 15xy + 20y = (-14 + 35y) Solving -8 + -6x + 15xy + 20y = -14 + 35y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + -6x + 15xy + 8 + 20y = -14 + 8 + 35y Reorder the terms: -8 + 8 + -6x + 15xy + 20y = -14 + 8 + 35y Combine like terms: -8 + 8 = 0 0 + -6x + 15xy + 20y = -14 + 8 + 35y -6x + 15xy + 20y = -14 + 8 + 35y Combine like terms: -14 + 8 = -6 -6x + 15xy + 20y = -6 + 35y Add '-20y' to each side of the equation. -6x + 15xy + 20y + -20y = -6 + 35y + -20y Combine like terms: 20y + -20y = 0 -6x + 15xy + 0 = -6 + 35y + -20y -6x + 15xy = -6 + 35y + -20y Combine like terms: 35y + -20y = 15y -6x + 15xy = -6 + 15y Reorder the terms: 6 + -6x + 15xy + -15y = -6 + 15y + 6 + -15y Reorder the terms: 6 + -6x + 15xy + -15y = -6 + 6 + 15y + -15y Combine like terms: -6 + 6 = 0 6 + -6x + 15xy + -15y = 0 + 15y + -15y 6 + -6x + 15xy + -15y = 15y + -15y Combine like terms: 15y + -15y = 0 6 + -6x + 15xy + -15y = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -2x + 5xy + -5y) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -2x + 5xy + -5y)' equal to zero and attempt to solve: Simplifying 2 + -2x + 5xy + -5y = 0 Solving 2 + -2x + 5xy + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2x + 5xy + -2 + -5y = 0 + -2 Reorder the terms: 2 + -2 + -2x + 5xy + -5y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2x + 5xy + -5y = 0 + -2 -2x + 5xy + -5y = 0 + -2 Combine like terms: 0 + -2 = -2 -2x + 5xy + -5y = -2 Add '5y' to each side of the equation. -2x + 5xy + -5y + 5y = -2 + 5y Combine like terms: -5y + 5y = 0 -2x + 5xy + 0 = -2 + 5y -2x + 5xy = -2 + 5y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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