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Simplifying 0 = a(x + -6)(x + -7)(x + -1b) Reorder the terms: 0 = a(-6 + x)(x + -7)(x + -1b) Reorder the terms: 0 = a(-6 + x)(-7 + x)(x + -1b) Reorder the terms: 0 = a(-6 + x)(-7 + x)(-1b + x) Multiply (-6 + x) * (-7 + x) 0 = a(-6(-7 + x) + x(-7 + x))(-1b + x) 0 = a((-7 * -6 + x * -6) + x(-7 + x))(-1b + x) 0 = a((42 + -6x) + x(-7 + x))(-1b + x) 0 = a(42 + -6x + (-7 * x + x * x))(-1b + x) 0 = a(42 + -6x + (-7x + x2))(-1b + x) Combine like terms: -6x + -7x = -13x 0 = a(42 + -13x + x2)(-1b + x) Multiply (42 + -13x + x2) * (-1b + x) 0 = a(42(-1b + x) + -13x * (-1b + x) + x2(-1b + x)) 0 = a((-1b * 42 + x * 42) + -13x * (-1b + x) + x2(-1b + x)) 0 = a((-42b + 42x) + -13x * (-1b + x) + x2(-1b + x)) 0 = a(-42b + 42x + (-1b * -13x + x * -13x) + x2(-1b + x)) 0 = a(-42b + 42x + (13bx + -13x2) + x2(-1b + x)) 0 = a(-42b + 42x + 13bx + -13x2 + (-1b * x2 + x * x2)) 0 = a(-42b + 42x + 13bx + -13x2 + (-1bx2 + x3)) Reorder the terms: 0 = a(-42b + 13bx + -1bx2 + 42x + -13x2 + x3) 0 = a(-42b + 13bx + -1bx2 + 42x + -13x2 + x3) 0 = (-42b * a + 13bx * a + -1bx2 * a + 42x * a + -13x2 * a + x3 * a) 0 = (-42ab + 13abx + -1abx2 + 42ax + -13ax2 + ax3) Solving 0 = -42ab + 13abx + -1abx2 + 42ax + -13ax2 + ax3 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '42ab' to each side of the equation. 0 + 42ab = -42ab + 13abx + -1abx2 + 42ax + -13ax2 + 42ab + ax3 Remove the zero: 42ab = -42ab + 13abx + -1abx2 + 42ax + -13ax2 + 42ab + ax3 Reorder the terms: 42ab = -42ab + 42ab + 13abx + -1abx2 + 42ax + -13ax2 + ax3 Combine like terms: -42ab + 42ab = 0 42ab = 0 + 13abx + -1abx2 + 42ax + -13ax2 + ax3 42ab = 13abx + -1abx2 + 42ax + -13ax2 + ax3 Add '-13abx' to each side of the equation. 42ab + -13abx = 13abx + -1abx2 + 42ax + -13ax2 + -13abx + ax3 Reorder the terms: 42ab + -13abx = 13abx + -13abx + -1abx2 + 42ax + -13ax2 + ax3 Combine like terms: 13abx + -13abx = 0 42ab + -13abx = 0 + -1abx2 + 42ax + -13ax2 + ax3 42ab + -13abx = -1abx2 + 42ax + -13ax2 + ax3 Add 'abx2' to each side of the equation. 42ab + -13abx + abx2 = -1abx2 + 42ax + -13ax2 + abx2 + ax3 Reorder the terms: 42ab + -13abx + abx2 = -1abx2 + abx2 + 42ax + -13ax2 + ax3 Combine like terms: -1abx2 + abx2 = 0 42ab + -13abx + abx2 = 0 + 42ax + -13ax2 + ax3 42ab + -13abx + abx2 = 42ax + -13ax2 + ax3 Add '-42ax' to each side of the equation. 42ab + -13abx + abx2 + -42ax = 42ax + -13ax2 + -42ax + ax3 Reorder the terms: 42ab + -13abx + abx2 + -42ax = 42ax + -42ax + -13ax2 + ax3 Combine like terms: 42ax + -42ax = 0 42ab + -13abx + abx2 + -42ax = 0 + -13ax2 + ax3 42ab + -13abx + abx2 + -42ax = -13ax2 + ax3 Add '13ax2' to each side of the equation. 42ab + -13abx + abx2 + -42ax + 13ax2 = -13ax2 + 13ax2 + ax3 Combine like terms: -13ax2 + 13ax2 = 0 42ab + -13abx + abx2 + -42ax + 13ax2 = 0 + ax3 42ab + -13abx + abx2 + -42ax + 13ax2 = ax3 Add '-1ax3' to each side of the equation. 42ab + -13abx + abx2 + -42ax + 13ax2 + -1ax3 = ax3 + -1ax3 Combine like terms: ax3 + -1ax3 = 0 42ab + -13abx + abx2 + -42ax + 13ax2 + -1ax3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(42b + -13bx + bx2 + -42x + 13x2 + -1x3) = 0Subproblem 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 '(42b + -13bx + bx2 + -42x + 13x2 + -1x3)' equal to zero and attempt to solve: Simplifying 42b + -13bx + bx2 + -42x + 13x2 + -1x3 = 0 Solving 42b + -13bx + bx2 + -42x + 13x2 + -1x3 = 0 Move all terms containing a to the left, all other terms to the right. Add '-42b' to each side of the equation. 42b + -13bx + bx2 + -42x + 13x2 + -42b + -1x3 = 0 + -42b Reorder the terms: 42b + -42b + -13bx + bx2 + -42x + 13x2 + -1x3 = 0 + -42b Combine like terms: 42b + -42b = 0 0 + -13bx + bx2 + -42x + 13x2 + -1x3 = 0 + -42b -13bx + bx2 + -42x + 13x2 + -1x3 = 0 + -42b Remove the zero: -13bx + bx2 + -42x + 13x2 + -1x3 = -42b Add '13bx' to each side of the equation. -13bx + bx2 + -42x + 13x2 + 13bx + -1x3 = -42b + 13bx Reorder the terms: -13bx + 13bx + bx2 + -42x + 13x2 + -1x3 = -42b + 13bx Combine like terms: -13bx + 13bx = 0 0 + bx2 + -42x + 13x2 + -1x3 = -42b + 13bx bx2 + -42x + 13x2 + -1x3 = -42b + 13bx Add '-1bx2' to each side of the equation. bx2 + -42x + 13x2 + -1bx2 + -1x3 = -42b + 13bx + -1bx2 Reorder the terms: bx2 + -1bx2 + -42x + 13x2 + -1x3 = -42b + 13bx + -1bx2 Combine like terms: bx2 + -1bx2 = 0 0 + -42x + 13x2 + -1x3 = -42b + 13bx + -1bx2 -42x + 13x2 + -1x3 = -42b + 13bx + -1bx2 Add '42x' to each side of the equation. -42x + 13x2 + 42x + -1x3 = -42b + 13bx + -1bx2 + 42x Reorder the terms: -42x + 42x + 13x2 + -1x3 = -42b + 13bx + -1bx2 + 42x Combine like terms: -42x + 42x = 0 0 + 13x2 + -1x3 = -42b + 13bx + -1bx2 + 42x 13x2 + -1x3 = -42b + 13bx + -1bx2 + 42x Add '-13x2' to each side of the equation. 13x2 + -13x2 + -1x3 = -42b + 13bx + -1bx2 + 42x + -13x2 Combine like terms: 13x2 + -13x2 = 0 0 + -1x3 = -42b + 13bx + -1bx2 + 42x + -13x2 -1x3 = -42b + 13bx + -1bx2 + 42x + -13x2 Add 'x3' to each side of the equation. -1x3 + x3 = -42b + 13bx + -1bx2 + 42x + -13x2 + x3 Combine like terms: -1x3 + x3 = 0 0 = -42b + 13bx + -1bx2 + 42x + -13x2 + x3 Simplifying 0 = -42b + 13bx + -1bx2 + 42x + -13x2 + x3 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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