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Simplifying 5x3 + 5x2r + -10xr = 0 Reorder the terms: -10rx + 5rx2 + 5x3 = 0 Solving -10rx + 5rx2 + 5x3 = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5x3' to each side of the equation. -10rx + 5rx2 + 5x3 + -5x3 = 0 + -5x3 Combine like terms: 5x3 + -5x3 = 0 -10rx + 5rx2 + 0 = 0 + -5x3 -10rx + 5rx2 = 0 + -5x3 Remove the zero: -10rx + 5rx2 = -5x3 Combine like terms: -5x3 + 5x3 = 0 -10rx + 5rx2 + 5x3 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(-2r + rx + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing r to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x 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 '(-2r + rx + x2)' equal to zero and attempt to solve: Simplifying -2r + rx + x2 = 0 Solving -2r + rx + x2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-1x2' to each side of the equation. -2r + rx + x2 + -1x2 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 -2r + rx + 0 = 0 + -1x2 -2r + rx = 0 + -1x2 Remove the zero: -2r + rx = -1x2 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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