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Simplifying 3ax + -4a2 = 12a2 + -1ax Reorder the terms: 3ax + -4a2 = -1ax + 12a2 Solving 3ax + -4a2 = -1ax + 12a2 Solving for variable 'a'. Reorder the terms: 3ax + ax + -4a2 + -12a2 = -1ax + 12a2 + ax + -12a2 Combine like terms: 3ax + ax = 4ax 4ax + -4a2 + -12a2 = -1ax + 12a2 + ax + -12a2 Combine like terms: -4a2 + -12a2 = -16a2 4ax + -16a2 = -1ax + 12a2 + ax + -12a2 Reorder the terms: 4ax + -16a2 = -1ax + ax + 12a2 + -12a2 Combine like terms: -1ax + ax = 0 4ax + -16a2 = 0 + 12a2 + -12a2 4ax + -16a2 = 12a2 + -12a2 Combine like terms: 12a2 + -12a2 = 0 4ax + -16a2 = 0 Factor out the Greatest Common Factor (GCF), '4a'. 4a(x + -4a) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(x + -4a)' equal to zero and attempt to solve: Simplifying x + -4a = 0 Reorder the terms: -4a + x = 0 Solving -4a + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. -4a + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 -4a + 0 = 0 + -1x -4a = 0 + -1x Remove the zero: -4a = -1x Divide each side by '-4'. a = 0.25x Simplifying a = 0.25xSolution
a = {0, 0.25x}
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