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Simplifying 5x3 + -5cx2 + 10x2 + -10xc = 0 Reorder the terms: -10cx + -5cx2 + 10x2 + 5x3 = 0 Solving -10cx + -5cx2 + 10x2 + 5x3 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-10x2' to each side of the equation. -10cx + -5cx2 + 10x2 + -10x2 + 5x3 = 0 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -10cx + -5cx2 + 0 + 5x3 = 0 + -10x2 -10cx + -5cx2 + 5x3 = 0 + -10x2 Remove the zero: -10cx + -5cx2 + 5x3 = -10x2 Add '-5x3' to each side of the equation. -10cx + -5cx2 + 5x3 + -5x3 = -10x2 + -5x3 Combine like terms: 5x3 + -5x3 = 0 -10cx + -5cx2 + 0 = -10x2 + -5x3 -10cx + -5cx2 = -10x2 + -5x3 Reorder the terms: -10cx + -5cx2 + 10x2 + 5x3 = -10x2 + 10x2 + -5x3 + 5x3 Combine like terms: -10x2 + 10x2 = 0 -10cx + -5cx2 + 10x2 + 5x3 = 0 + -5x3 + 5x3 -10cx + -5cx2 + 10x2 + 5x3 = -5x3 + 5x3 Combine like terms: -5x3 + 5x3 = 0 -10cx + -5cx2 + 10x2 + 5x3 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(-2c + -1cx + 2x + 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 c 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 '(-2c + -1cx + 2x + x2)' equal to zero and attempt to solve: Simplifying -2c + -1cx + 2x + x2 = 0 Solving -2c + -1cx + 2x + x2 = 0 Move all terms containing c to the left, all other terms to the right. Add '-2x' to each side of the equation. -2c + -1cx + 2x + -2x + x2 = 0 + -2x Combine like terms: 2x + -2x = 0 -2c + -1cx + 0 + x2 = 0 + -2x -2c + -1cx + x2 = 0 + -2x Remove the zero: -2c + -1cx + x2 = -2x Add '-1x2' to each side of the equation. -2c + -1cx + x2 + -1x2 = -2x + -1x2 Combine like terms: x2 + -1x2 = 0 -2c + -1cx + 0 = -2x + -1x2 -2c + -1cx = -2x + -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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