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Simplifying 3(x + -1a)(x + -5) + 33(x + a)(x + -5) = 6(x + a)(x + -1a) Reorder the terms: 3(-1a + x)(x + -5) + 33(x + a)(x + -5) = 6(x + a)(x + -1a) Reorder the terms: 3(-1a + x)(-5 + x) + 33(x + a)(x + -5) = 6(x + a)(x + -1a) Multiply (-1a + x) * (-5 + x) 3(-1a * (-5 + x) + x(-5 + x)) + 33(x + a)(x + -5) = 6(x + a)(x + -1a) 3((-5 * -1a + x * -1a) + x(-5 + x)) + 33(x + a)(x + -5) = 6(x + a)(x + -1a) 3((5a + -1ax) + x(-5 + x)) + 33(x + a)(x + -5) = 6(x + a)(x + -1a) 3(5a + -1ax + (-5 * x + x * x)) + 33(x + a)(x + -5) = 6(x + a)(x + -1a) 3(5a + -1ax + (-5x + x2)) + 33(x + a)(x + -5) = 6(x + a)(x + -1a) 3(5a + -1ax + -5x + x2) + 33(x + a)(x + -5) = 6(x + a)(x + -1a) (5a * 3 + -1ax * 3 + -5x * 3 + x2 * 3) + 33(x + a)(x + -5) = 6(x + a)(x + -1a) (15a + -3ax + -15x + 3x2) + 33(x + a)(x + -5) = 6(x + a)(x + -1a) Reorder the terms: 15a + -3ax + -15x + 3x2 + 33(a + x)(x + -5) = 6(x + a)(x + -1a) Reorder the terms: 15a + -3ax + -15x + 3x2 + 33(a + x)(-5 + x) = 6(x + a)(x + -1a) Multiply (a + x) * (-5 + x) 15a + -3ax + -15x + 3x2 + 33(a(-5 + x) + x(-5 + x)) = 6(x + a)(x + -1a) 15a + -3ax + -15x + 3x2 + 33((-5 * a + x * a) + x(-5 + x)) = 6(x + a)(x + -1a) 15a + -3ax + -15x + 3x2 + 33((-5a + ax) + x(-5 + x)) = 6(x + a)(x + -1a) 15a + -3ax + -15x + 3x2 + 33(-5a + ax + (-5 * x + x * x)) = 6(x + a)(x + -1a) 15a + -3ax + -15x + 3x2 + 33(-5a + ax + (-5x + x2)) = 6(x + a)(x + -1a) 15a + -3ax + -15x + 3x2 + 33(-5a + ax + -5x + x2) = 6(x + a)(x + -1a) 15a + -3ax + -15x + 3x2 + (-5a * 33 + ax * 33 + -5x * 33 + x2 * 33) = 6(x + a)(x + -1a) 15a + -3ax + -15x + 3x2 + (-165a + 33ax + -165x + 33x2) = 6(x + a)(x + -1a) Reorder the terms: 15a + -165a + -3ax + 33ax + -15x + -165x + 3x2 + 33x2 = 6(x + a)(x + -1a) Combine like terms: 15a + -165a = -150a -150a + -3ax + 33ax + -15x + -165x + 3x2 + 33x2 = 6(x + a)(x + -1a) Combine like terms: -3ax + 33ax = 30ax -150a + 30ax + -15x + -165x + 3x2 + 33x2 = 6(x + a)(x + -1a) Combine like terms: -15x + -165x = -180x -150a + 30ax + -180x + 3x2 + 33x2 = 6(x + a)(x + -1a) Combine like terms: 3x2 + 33x2 = 36x2 -150a + 30ax + -180x + 36x2 = 6(x + a)(x + -1a) Reorder the terms: -150a + 30ax + -180x + 36x2 = 6(a + x)(x + -1a) Reorder the terms: -150a + 30ax + -180x + 36x2 = 6(a + x)(-1a + x) Multiply (a + x) * (-1a + x) -150a + 30ax + -180x + 36x2 = 6(a(-1a + x) + x(-1a + x)) -150a + 30ax + -180x + 36x2 = 6((-1a * a + x * a) + x(-1a + x)) Reorder the terms: -150a + 30ax + -180x + 36x2 = 6((ax + -1a2) + x(-1a + x)) -150a + 30ax + -180x + 36x2 = 6((ax + -1a2) + x(-1a + x)) -150a + 30ax + -180x + 36x2 = 6(ax + -1a2 + (-1a * x + x * x)) -150a + 30ax + -180x + 36x2 = 6(ax + -1a2 + (-1ax + x2)) Reorder the terms: -150a + 30ax + -180x + 36x2 = 6(ax + -1ax + -1a2 + x2) Combine like terms: ax + -1ax = 0 -150a + 30ax + -180x + 36x2 = 6(0 + -1a2 + x2) -150a + 30ax + -180x + 36x2 = 6(-1a2 + x2) -150a + 30ax + -180x + 36x2 = (-1a2 * 6 + x2 * 6) -150a + 30ax + -180x + 36x2 = (-6a2 + 6x2) Solving -150a + 30ax + -180x + 36x2 = -6a2 + 6x2 Solving for variable 'a'. Reorder the terms: -150a + 30ax + 6a2 + -180x + 36x2 + -6x2 = -6a2 + 6x2 + 6a2 + -6x2 Combine like terms: 36x2 + -6x2 = 30x2 -150a + 30ax + 6a2 + -180x + 30x2 = -6a2 + 6x2 + 6a2 + -6x2 Reorder the terms: -150a + 30ax + 6a2 + -180x + 30x2 = -6a2 + 6a2 + 6x2 + -6x2 Combine like terms: -6a2 + 6a2 = 0 -150a + 30ax + 6a2 + -180x + 30x2 = 0 + 6x2 + -6x2 -150a + 30ax + 6a2 + -180x + 30x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -150a + 30ax + 6a2 + -180x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-25a + 5ax + a2 + -30x + 5x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-25a + 5ax + a2 + -30x + 5x2)' equal to zero and attempt to solve: Simplifying -25a + 5ax + a2 + -30x + 5x2 = 0 Solving -25a + 5ax + a2 + -30x + 5x2 = 0 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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