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Simplifying X(2x + -6) + x(4x + -3) = (6x + 9)(x + -6) Reorder the terms: X(-6 + 2x) + x(4x + -3) = (6x + 9)(x + -6) (-6 * X + 2x * X) + x(4x + -3) = (6x + 9)(x + -6) (-6X + 2xX) + x(4x + -3) = (6x + 9)(x + -6) Reorder the terms: -6X + 2xX + x(-3 + 4x) = (6x + 9)(x + -6) -6X + 2xX + (-3 * x + 4x * x) = (6x + 9)(x + -6) -6X + 2xX + (-3x + 4x2) = (6x + 9)(x + -6) Reorder the terms: -6X + -3x + 2xX + 4x2 = (6x + 9)(x + -6) Reorder the terms: -6X + -3x + 2xX + 4x2 = (9 + 6x)(x + -6) Reorder the terms: -6X + -3x + 2xX + 4x2 = (9 + 6x)(-6 + x) Multiply (9 + 6x) * (-6 + x) -6X + -3x + 2xX + 4x2 = (9(-6 + x) + 6x * (-6 + x)) -6X + -3x + 2xX + 4x2 = ((-6 * 9 + x * 9) + 6x * (-6 + x)) -6X + -3x + 2xX + 4x2 = ((-54 + 9x) + 6x * (-6 + x)) -6X + -3x + 2xX + 4x2 = (-54 + 9x + (-6 * 6x + x * 6x)) -6X + -3x + 2xX + 4x2 = (-54 + 9x + (-36x + 6x2)) Combine like terms: 9x + -36x = -27x -6X + -3x + 2xX + 4x2 = (-54 + -27x + 6x2) Solving -6X + -3x + 2xX + 4x2 = -54 + -27x + 6x2 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3x' to each side of the equation. -6X + -3x + 2xX + 3x + 4x2 = -54 + -27x + 3x + 6x2 Reorder the terms: -6X + -3x + 3x + 2xX + 4x2 = -54 + -27x + 3x + 6x2 Combine like terms: -3x + 3x = 0 -6X + 0 + 2xX + 4x2 = -54 + -27x + 3x + 6x2 -6X + 2xX + 4x2 = -54 + -27x + 3x + 6x2 Combine like terms: -27x + 3x = -24x -6X + 2xX + 4x2 = -54 + -24x + 6x2 Add '-4x2' to each side of the equation. -6X + 2xX + 4x2 + -4x2 = -54 + -24x + 6x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -6X + 2xX + 0 = -54 + -24x + 6x2 + -4x2 -6X + 2xX = -54 + -24x + 6x2 + -4x2 Combine like terms: 6x2 + -4x2 = 2x2 -6X + 2xX = -54 + -24x + 2x2 Reorder the terms: 54 + -6X + 24x + 2xX + -2x2 = -54 + -24x + 2x2 + 54 + 24x + -2x2 Reorder the terms: 54 + -6X + 24x + 2xX + -2x2 = -54 + 54 + -24x + 24x + 2x2 + -2x2 Combine like terms: -54 + 54 = 0 54 + -6X + 24x + 2xX + -2x2 = 0 + -24x + 24x + 2x2 + -2x2 54 + -6X + 24x + 2xX + -2x2 = -24x + 24x + 2x2 + -2x2 Combine like terms: -24x + 24x = 0 54 + -6X + 24x + 2xX + -2x2 = 0 + 2x2 + -2x2 54 + -6X + 24x + 2xX + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 54 + -6X + 24x + 2xX + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -3X + 12x + xX + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + -3X + 12x + xX + -1x2)' equal to zero and attempt to solve: Simplifying 27 + -3X + 12x + xX + -1x2 = 0 Solving 27 + -3X + 12x + xX + -1x2 = 0 Move all terms containing X to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -3X + 12x + xX + -27 + -1x2 = 0 + -27 Reorder the terms: 27 + -27 + -3X + 12x + xX + -1x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -3X + 12x + xX + -1x2 = 0 + -27 -3X + 12x + xX + -1x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -3X + 12x + xX + -1x2 = -27 Add '-12x' to each side of the equation. -3X + 12x + xX + -12x + -1x2 = -27 + -12x Reorder the terms: -3X + 12x + -12x + xX + -1x2 = -27 + -12x Combine like terms: 12x + -12x = 0 -3X + 0 + xX + -1x2 = -27 + -12x -3X + xX + -1x2 = -27 + -12x Add 'x2' to each side of the equation. -3X + xX + -1x2 + x2 = -27 + -12x + x2 Combine like terms: -1x2 + x2 = 0 -3X + xX + 0 = -27 + -12x + x2 -3X + xX = -27 + -12x + x2 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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