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Simplifying 10xy + 15y * 2 + 8wx + 12wy = (2x + 3y)(5y + 4w) Reorder the terms for easier multiplication: 10xy + 15 * 2y + 8wx + 12wy = (2x + 3y)(5y + 4w) Multiply 15 * 2 10xy + 30y + 8wx + 12wy = (2x + 3y)(5y + 4w) Reorder the terms: 8wx + 12wy + 10xy + 30y = (2x + 3y)(5y + 4w) Reorder the terms: 8wx + 12wy + 10xy + 30y = (2x + 3y)(4w + 5y) Multiply (2x + 3y) * (4w + 5y) 8wx + 12wy + 10xy + 30y = (2x * (4w + 5y) + 3y * (4w + 5y)) 8wx + 12wy + 10xy + 30y = ((4w * 2x + 5y * 2x) + 3y * (4w + 5y)) 8wx + 12wy + 10xy + 30y = ((8wx + 10xy) + 3y * (4w + 5y)) 8wx + 12wy + 10xy + 30y = (8wx + 10xy + (4w * 3y + 5y * 3y)) 8wx + 12wy + 10xy + 30y = (8wx + 10xy + (12wy + 15y2)) Reorder the terms: 8wx + 12wy + 10xy + 30y = (8wx + 12wy + 10xy + 15y2) 8wx + 12wy + 10xy + 30y = (8wx + 12wy + 10xy + 15y2) Add '-8wx' to each side of the equation. 8wx + 12wy + 10xy + -8wx + 30y = 8wx + 12wy + 10xy + -8wx + 15y2 Reorder the terms: 8wx + -8wx + 12wy + 10xy + 30y = 8wx + 12wy + 10xy + -8wx + 15y2 Combine like terms: 8wx + -8wx = 0 0 + 12wy + 10xy + 30y = 8wx + 12wy + 10xy + -8wx + 15y2 12wy + 10xy + 30y = 8wx + 12wy + 10xy + -8wx + 15y2 Reorder the terms: 12wy + 10xy + 30y = 8wx + -8wx + 12wy + 10xy + 15y2 Combine like terms: 8wx + -8wx = 0 12wy + 10xy + 30y = 0 + 12wy + 10xy + 15y2 12wy + 10xy + 30y = 12wy + 10xy + 15y2 Add '-12wy' to each side of the equation. 12wy + 10xy + -12wy + 30y = 12wy + 10xy + -12wy + 15y2 Reorder the terms: 12wy + -12wy + 10xy + 30y = 12wy + 10xy + -12wy + 15y2 Combine like terms: 12wy + -12wy = 0 0 + 10xy + 30y = 12wy + 10xy + -12wy + 15y2 10xy + 30y = 12wy + 10xy + -12wy + 15y2 Reorder the terms: 10xy + 30y = 12wy + -12wy + 10xy + 15y2 Combine like terms: 12wy + -12wy = 0 10xy + 30y = 0 + 10xy + 15y2 10xy + 30y = 10xy + 15y2 Add '-10xy' to each side of the equation. 10xy + -10xy + 30y = 10xy + -10xy + 15y2 Combine like terms: 10xy + -10xy = 0 0 + 30y = 10xy + -10xy + 15y2 30y = 10xy + -10xy + 15y2 Combine like terms: 10xy + -10xy = 0 30y = 0 + 15y2 30y = 15y2 Solving 30y = 15y2 Solving for variable 'y'. Combine like terms: 15y2 + -15y2 = 0 30y + -15y2 = 0 Factor out the Greatest Common Factor (GCF), '15y'. 15y(2 + -1y) = 0 Ignore the factor 15.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Solution
y = {0, 2}
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