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Simplifying (a + b + -1c)(x + -3) + -1(b + -1c + -1a)(x + -3) = 0 Reorder the terms: (a + b + -1c)(-3 + x) + -1(b + -1c + -1a)(x + -3) = 0 Multiply (a + b + -1c) * (-3 + x) (a(-3 + x) + b(-3 + x) + -1c * (-3 + x)) + -1(b + -1c + -1a)(x + -3) = 0 ((-3 * a + x * a) + b(-3 + x) + -1c * (-3 + x)) + -1(b + -1c + -1a)(x + -3) = 0 ((-3a + ax) + b(-3 + x) + -1c * (-3 + x)) + -1(b + -1c + -1a)(x + -3) = 0 (-3a + ax + (-3 * b + x * b) + -1c * (-3 + x)) + -1(b + -1c + -1a)(x + -3) = 0 (-3a + ax + (-3b + bx) + -1c * (-3 + x)) + -1(b + -1c + -1a)(x + -3) = 0 (-3a + ax + -3b + bx + (-3 * -1c + x * -1c)) + -1(b + -1c + -1a)(x + -3) = 0 (-3a + ax + -3b + bx + (3c + -1cx)) + -1(b + -1c + -1a)(x + -3) = 0 (-3a + ax + -3b + bx + 3c + -1cx) + -1(b + -1c + -1a)(x + -3) = 0 Reorder the terms: -3a + ax + -3b + bx + 3c + -1cx + -1(-1a + b + -1c)(x + -3) = 0 Reorder the terms: -3a + ax + -3b + bx + 3c + -1cx + -1(-1a + b + -1c)(-3 + x) = 0 Multiply (-1a + b + -1c) * (-3 + x) -3a + ax + -3b + bx + 3c + -1cx + -1(-1a * (-3 + x) + b(-3 + x) + -1c * (-3 + x)) = 0 -3a + ax + -3b + bx + 3c + -1cx + -1((-3 * -1a + x * -1a) + b(-3 + x) + -1c * (-3 + x)) = 0 -3a + ax + -3b + bx + 3c + -1cx + -1((3a + -1ax) + b(-3 + x) + -1c * (-3 + x)) = 0 -3a + ax + -3b + bx + 3c + -1cx + -1(3a + -1ax + (-3 * b + x * b) + -1c * (-3 + x)) = 0 -3a + ax + -3b + bx + 3c + -1cx + -1(3a + -1ax + (-3b + bx) + -1c * (-3 + x)) = 0 -3a + ax + -3b + bx + 3c + -1cx + -1(3a + -1ax + -3b + bx + (-3 * -1c + x * -1c)) = 0 -3a + ax + -3b + bx + 3c + -1cx + -1(3a + -1ax + -3b + bx + (3c + -1cx)) = 0 -3a + ax + -3b + bx + 3c + -1cx + -1(3a + -1ax + -3b + bx + 3c + -1cx) = 0 -3a + ax + -3b + bx + 3c + -1cx + (3a * -1 + -1ax * -1 + -3b * -1 + bx * -1 + 3c * -1 + -1cx * -1) = 0 -3a + ax + -3b + bx + 3c + -1cx + (-3a + 1ax + 3b + -1bx + -3c + 1cx) = 0 Reorder the terms: -3a + -3a + ax + 1ax + -3b + 3b + bx + -1bx + 3c + -3c + -1cx + 1cx = 0 Combine like terms: -3a + -3a = -6a -6a + ax + 1ax + -3b + 3b + bx + -1bx + 3c + -3c + -1cx + 1cx = 0 Combine like terms: ax + 1ax = 2ax -6a + 2ax + -3b + 3b + bx + -1bx + 3c + -3c + -1cx + 1cx = 0 Combine like terms: -3b + 3b = 0 -6a + 2ax + 0 + bx + -1bx + 3c + -3c + -1cx + 1cx = 0 -6a + 2ax + bx + -1bx + 3c + -3c + -1cx + 1cx = 0 Combine like terms: bx + -1bx = 0 -6a + 2ax + 0 + 3c + -3c + -1cx + 1cx = 0 -6a + 2ax + 3c + -3c + -1cx + 1cx = 0 Combine like terms: 3c + -3c = 0 -6a + 2ax + 0 + -1cx + 1cx = 0 -6a + 2ax + -1cx + 1cx = 0 Combine like terms: -1cx + 1cx = 0 -6a + 2ax + 0 = 0 -6a + 2ax = 0 Solving -6a + 2ax = 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), '2a'. 2a(-3 + x) = 0 Ignore the factor 2.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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x 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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