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Simplifying 3x5y2 + -1875xy2 = 3xy2(x + -25)(x + 25) Reorder the terms: -1875xy2 + 3x5y2 = 3xy2(x + -25)(x + 25) Reorder the terms: -1875xy2 + 3x5y2 = 3xy2(-25 + x)(x + 25) Reorder the terms: -1875xy2 + 3x5y2 = 3xy2(-25 + x)(25 + x) Multiply (-25 + x) * (25 + x) -1875xy2 + 3x5y2 = 3xy2(-25(25 + x) + x(25 + x)) -1875xy2 + 3x5y2 = 3xy2((25 * -25 + x * -25) + x(25 + x)) -1875xy2 + 3x5y2 = 3xy2((-625 + -25x) + x(25 + x)) -1875xy2 + 3x5y2 = 3xy2(-625 + -25x + (25 * x + x * x)) -1875xy2 + 3x5y2 = 3xy2(-625 + -25x + (25x + x2)) Combine like terms: -25x + 25x = 0 -1875xy2 + 3x5y2 = 3xy2(-625 + 0 + x2) -1875xy2 + 3x5y2 = 3xy2(-625 + x2) -1875xy2 + 3x5y2 = (-625 * 3xy2 + x2 * 3xy2) -1875xy2 + 3x5y2 = (-1875xy2 + 3x3y2) Add '1875xy2' to each side of the equation. -1875xy2 + 1875xy2 + 3x5y2 = -1875xy2 + 1875xy2 + 3x3y2 Combine like terms: -1875xy2 + 1875xy2 = 0 0 + 3x5y2 = -1875xy2 + 1875xy2 + 3x3y2 3x5y2 = -1875xy2 + 1875xy2 + 3x3y2 Combine like terms: -1875xy2 + 1875xy2 = 0 3x5y2 = 0 + 3x3y2 3x5y2 = 3x3y2 Solving 3x5y2 = 3x3y2 Solving for variable 'x'. Reorder the terms: -3x3y2 + 3x5y2 = 3x3y2 + -3x3y2 Combine like terms: 3x3y2 + -3x3y2 = 0 -3x3y2 + 3x5y2 = 0 Factor out the Greatest Common Factor (GCF), '3x3y2'. 3x3y2(-1 + x2) = 0 Factor a difference between two squares. 3x3y2((1 + x)(-1 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x3y2' equal to zero and attempt to solve: Simplifying x3y2 = 0 Solving x3y2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3y2 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 3
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Solution
x = {-1, 1}
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