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Simplifying ax(x + 12)(x + -7) = 0 Reorder the terms: ax(12 + x)(x + -7) = 0 Reorder the terms: ax(12 + x)(-7 + x) = 0 Multiply (12 + x) * (-7 + x) ax(12(-7 + x) + x(-7 + x)) = 0 ax((-7 * 12 + x * 12) + x(-7 + x)) = 0 ax((-84 + 12x) + x(-7 + x)) = 0 ax(-84 + 12x + (-7 * x + x * x)) = 0 ax(-84 + 12x + (-7x + x2)) = 0 Combine like terms: 12x + -7x = 5x ax(-84 + 5x + x2) = 0 (-84 * ax + 5x * ax + x2 * ax) = 0 (-84ax + 5ax2 + ax3) = 0 Solving -84ax + 5ax2 + ax3 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ax'. ax(-84 + 5x + x2) = 0 Factor a trinomial. ax((-12 + -1x)(7 + -1x)) = 0Subproblem 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 '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Add 'x' to each side of the equation. -1x + x = 12 + x Combine like terms: -1x + x = 0 0 = 12 + x Simplifying 0 = 12 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + x 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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