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Simplifying 0 = ax(x + 1) Reorder the terms: 0 = ax(1 + x) 0 = (1 * ax + x * ax) 0 = (1ax + ax2) Solving 0 = 1ax + ax2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1ax' to each side of the equation. 0 + -1ax = 1ax + -1ax + ax2 Remove the zero: -1ax = 1ax + -1ax + ax2 Combine like terms: 1ax + -1ax = 0 -1ax = 0 + ax2 -1ax = ax2 Add '-1ax2' to each side of the equation. -1ax + -1ax2 = ax2 + -1ax2 Combine like terms: ax2 + -1ax2 = 0 -1ax + -1ax2 = 0 Factor out the Greatest Common Factor (GCF), '-1ax'. -1ax(1 + x) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'ax' equal to zero and attempt to solve: Simplifying ax = 0 Solving ax = 0 Move all terms containing a to the left, all other terms to the right. Simplifying ax = 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 a 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 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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