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Simplifying 23a + -1(5ax + -1[9ax + (12a + -6ax)] + -1(3a + -8ax)) + -15a = 5ax + -7a Remove parenthesis around (12a + -6ax) 23a + -1(5ax + -1[9ax + 12a + -6ax] + -1(3a + -8ax)) + -15a = 5ax + -7a Reorder the terms: 23a + -1(5ax + -1[12a + 9ax + -6ax] + -1(3a + -8ax)) + -15a = 5ax + -7a Combine like terms: 9ax + -6ax = 3ax 23a + -1(5ax + -1[12a + 3ax] + -1(3a + -8ax)) + -15a = 5ax + -7a 23a + -1(5ax + [12a * -1 + 3ax * -1] + -1(3a + -8ax)) + -15a = 5ax + -7a 23a + -1(5ax + [-12a + -3ax] + -1(3a + -8ax)) + -15a = 5ax + -7a 23a + -1(5ax + -12a + -3ax + (3a * -1 + -8ax * -1)) + -15a = 5ax + -7a 23a + -1(5ax + -12a + -3ax + (-3a + 8ax)) + -15a = 5ax + -7a Reorder the terms: 23a + -1(-12a + -3a + 5ax + -3ax + 8ax) + -15a = 5ax + -7a Combine like terms: -12a + -3a = -15a 23a + -1(-15a + 5ax + -3ax + 8ax) + -15a = 5ax + -7a Combine like terms: 5ax + -3ax = 2ax 23a + -1(-15a + 2ax + 8ax) + -15a = 5ax + -7a Combine like terms: 2ax + 8ax = 10ax 23a + -1(-15a + 10ax) + -15a = 5ax + -7a 23a + (-15a * -1 + 10ax * -1) + -15a = 5ax + -7a 23a + (15a + -10ax) + -15a = 5ax + -7a Reorder the terms: 23a + 15a + -15a + -10ax = 5ax + -7a Combine like terms: 23a + 15a = 38a 38a + -15a + -10ax = 5ax + -7a Combine like terms: 38a + -15a = 23a 23a + -10ax = 5ax + -7a Reorder the terms: 23a + -10ax = -7a + 5ax Solving 23a + -10ax = -7a + 5ax Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7a' to each side of the equation. 23a + 7a + -10ax = -7a + 7a + 5ax Combine like terms: 23a + 7a = 30a 30a + -10ax = -7a + 7a + 5ax Combine like terms: -7a + 7a = 0 30a + -10ax = 0 + 5ax 30a + -10ax = 5ax Add '-5ax' to each side of the equation. 30a + -10ax + -5ax = 5ax + -5ax Combine like terms: -10ax + -5ax = -15ax 30a + -15ax = 5ax + -5ax Combine like terms: 5ax + -5ax = 0 30a + -15ax = 0 Factor out the Greatest Common Factor (GCF), '15a'. 15a(2 + -1x) = 0 Ignore the factor 15.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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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