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Simplifying 15x(y + 3) = (4x + -5) * x(5y + -7) Reorder the terms: 15x(3 + y) = (4x + -5) * x(5y + -7) (3 * 15x + y * 15x) = (4x + -5) * x(5y + -7) (45x + 15xy) = (4x + -5) * x(5y + -7) Reorder the terms: 45x + 15xy = (-5 + 4x) * x(5y + -7) Reorder the terms: 45x + 15xy = (-5 + 4x) * x(-7 + 5y) Reorder the terms for easier multiplication: 45x + 15xy = x(-5 + 4x)(-7 + 5y) Multiply (-5 + 4x) * (-7 + 5y) 45x + 15xy = x(-5(-7 + 5y) + 4x * (-7 + 5y)) 45x + 15xy = x((-7 * -5 + 5y * -5) + 4x * (-7 + 5y)) 45x + 15xy = x((35 + -25y) + 4x * (-7 + 5y)) 45x + 15xy = x(35 + -25y + (-7 * 4x + 5y * 4x)) 45x + 15xy = x(35 + -25y + (-28x + 20xy)) Reorder the terms: 45x + 15xy = x(35 + -28x + 20xy + -25y) 45x + 15xy = x(35 + -28x + 20xy + -25y) 45x + 15xy = (35 * x + -28x * x + 20xy * x + -25y * x) Reorder the terms: 45x + 15xy = (35x + -25xy + -28x2 + 20x2y) 45x + 15xy = (35x + -25xy + -28x2 + 20x2y) Solving 45x + 15xy = 35x + -25xy + -28x2 + 20x2y Solving for variable 'x'. Reorder the terms: 45x + -35x + 15xy + 25xy + 28x2 + -20x2y = 35x + -25xy + -28x2 + 20x2y + -35x + 25xy + 28x2 + -20x2y Combine like terms: 45x + -35x = 10x 10x + 15xy + 25xy + 28x2 + -20x2y = 35x + -25xy + -28x2 + 20x2y + -35x + 25xy + 28x2 + -20x2y Combine like terms: 15xy + 25xy = 40xy 10x + 40xy + 28x2 + -20x2y = 35x + -25xy + -28x2 + 20x2y + -35x + 25xy + 28x2 + -20x2y Reorder the terms: 10x + 40xy + 28x2 + -20x2y = 35x + -35x + -25xy + 25xy + -28x2 + 28x2 + 20x2y + -20x2y Combine like terms: 35x + -35x = 0 10x + 40xy + 28x2 + -20x2y = 0 + -25xy + 25xy + -28x2 + 28x2 + 20x2y + -20x2y 10x + 40xy + 28x2 + -20x2y = -25xy + 25xy + -28x2 + 28x2 + 20x2y + -20x2y Combine like terms: -25xy + 25xy = 0 10x + 40xy + 28x2 + -20x2y = 0 + -28x2 + 28x2 + 20x2y + -20x2y 10x + 40xy + 28x2 + -20x2y = -28x2 + 28x2 + 20x2y + -20x2y Combine like terms: -28x2 + 28x2 = 0 10x + 40xy + 28x2 + -20x2y = 0 + 20x2y + -20x2y 10x + 40xy + 28x2 + -20x2y = 20x2y + -20x2y Combine like terms: 20x2y + -20x2y = 0 10x + 40xy + 28x2 + -20x2y = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(5 + 20y + 14x + -10xy) = 0 Ignore the factor 2.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 + 20y + 14x + -10xy)' equal to zero and attempt to solve: Simplifying 5 + 20y + 14x + -10xy = 0 Reorder the terms: 5 + 14x + -10xy + 20y = 0 Solving 5 + 14x + -10xy + 20y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 14x + -10xy + -5 + 20y = 0 + -5 Reorder the terms: 5 + -5 + 14x + -10xy + 20y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 14x + -10xy + 20y = 0 + -5 14x + -10xy + 20y = 0 + -5 Combine like terms: 0 + -5 = -5 14x + -10xy + 20y = -5 Add '-20y' to each side of the equation. 14x + -10xy + 20y + -20y = -5 + -20y Combine like terms: 20y + -20y = 0 14x + -10xy + 0 = -5 + -20y 14x + -10xy = -5 + -20y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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