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Simplifying 6x3(a + -1b) + x(b + -1a) = 0 (a * 6x3 + -1b * 6x3) + x(b + -1a) = 0 (6ax3 + -6bx3) + x(b + -1a) = 0 Reorder the terms: 6ax3 + -6bx3 + x(-1a + b) = 0 6ax3 + -6bx3 + (-1a * x + b * x) = 0 6ax3 + -6bx3 + (-1ax + bx) = 0 Reorder the terms: -1ax + 6ax3 + bx + -6bx3 = 0 Solving -1ax + 6ax3 + bx + -6bx3 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bx' to each side of the equation. -1ax + 6ax3 + bx + -1bx + -6bx3 = 0 + -1bx Combine like terms: bx + -1bx = 0 -1ax + 6ax3 + 0 + -6bx3 = 0 + -1bx -1ax + 6ax3 + -6bx3 = 0 + -1bx Remove the zero: -1ax + 6ax3 + -6bx3 = -1bx Add '6bx3' to each side of the equation. -1ax + 6ax3 + -6bx3 + 6bx3 = -1bx + 6bx3 Combine like terms: -6bx3 + 6bx3 = 0 -1ax + 6ax3 + 0 = -1bx + 6bx3 -1ax + 6ax3 = -1bx + 6bx3 Reorder the terms: -1ax + 6ax3 + bx + -6bx3 = -1bx + bx + 6bx3 + -6bx3 Combine like terms: -1bx + bx = 0 -1ax + 6ax3 + bx + -6bx3 = 0 + 6bx3 + -6bx3 -1ax + 6ax3 + bx + -6bx3 = 6bx3 + -6bx3 Combine like terms: 6bx3 + -6bx3 = 0 -1ax + 6ax3 + bx + -6bx3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1a + 6ax2 + b + -6bx2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1a + 6ax2 + b + -6bx2)' equal to zero and attempt to solve: Simplifying -1a + 6ax2 + b + -6bx2 = 0 Solving -1a + 6ax2 + b + -6bx2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. -1a + 6ax2 + b + -1b + -6bx2 = 0 + -1b Combine like terms: b + -1b = 0 -1a + 6ax2 + 0 + -6bx2 = 0 + -1b -1a + 6ax2 + -6bx2 = 0 + -1b Remove the zero: -1a + 6ax2 + -6bx2 = -1b Add '6bx2' to each side of the equation. -1a + 6ax2 + -6bx2 + 6bx2 = -1b + 6bx2 Combine like terms: -6bx2 + 6bx2 = 0 -1a + 6ax2 + 0 = -1b + 6bx2 -1a + 6ax2 = -1b + 6bx2 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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