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Simplifying (2x + 3)(3x + -2) = 6x * 2 + nx + -6 Reorder the terms: (3 + 2x)(3x + -2) = 6x * 2 + nx + -6 Reorder the terms: (3 + 2x)(-2 + 3x) = 6x * 2 + nx + -6 Multiply (3 + 2x) * (-2 + 3x) (3(-2 + 3x) + 2x * (-2 + 3x)) = 6x * 2 + nx + -6 ((-2 * 3 + 3x * 3) + 2x * (-2 + 3x)) = 6x * 2 + nx + -6 ((-6 + 9x) + 2x * (-2 + 3x)) = 6x * 2 + nx + -6 (-6 + 9x + (-2 * 2x + 3x * 2x)) = 6x * 2 + nx + -6 (-6 + 9x + (-4x + 6x2)) = 6x * 2 + nx + -6 Combine like terms: 9x + -4x = 5x (-6 + 5x + 6x2) = 6x * 2 + nx + -6 Reorder the terms for easier multiplication: -6 + 5x + 6x2 = 6 * 2x + nx + -6 Multiply 6 * 2 -6 + 5x + 6x2 = 12x + nx + -6 Reorder the terms: -6 + 5x + 6x2 = -6 + nx + 12x Add '6' to each side of the equation. -6 + 5x + 6 + 6x2 = -6 + nx + 6 + 12x Reorder the terms: -6 + 6 + 5x + 6x2 = -6 + nx + 6 + 12x Combine like terms: -6 + 6 = 0 0 + 5x + 6x2 = -6 + nx + 6 + 12x 5x + 6x2 = -6 + nx + 6 + 12x Reorder the terms: 5x + 6x2 = -6 + 6 + nx + 12x Combine like terms: -6 + 6 = 0 5x + 6x2 = 0 + nx + 12x 5x + 6x2 = nx + 12x Solving 5x + 6x2 = nx + 12x Solving for variable 'x'. Reorder the terms: -1nx + 5x + -12x + 6x2 = nx + 12x + -1nx + -12x Combine like terms: 5x + -12x = -7x -1nx + -7x + 6x2 = nx + 12x + -1nx + -12x Reorder the terms: -1nx + -7x + 6x2 = nx + -1nx + 12x + -12x Combine like terms: nx + -1nx = 0 -1nx + -7x + 6x2 = 0 + 12x + -12x -1nx + -7x + 6x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -1nx + -7x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1n + -7 + 6x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1n + -7 + 6x)' equal to zero and attempt to solve: Simplifying -1n + -7 + 6x = 0 Reorder the terms: -7 + -1n + 6x = 0 Solving -7 + -1n + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + -1n + 7 + 6x = 0 + 7 Reorder the terms: -7 + 7 + -1n + 6x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n + 6x = 0 + 7 -1n + 6x = 0 + 7 Combine like terms: 0 + 7 = 7 -1n + 6x = 7 Add 'n' to each side of the equation. -1n + n + 6x = 7 + n Combine like terms: -1n + n = 0 0 + 6x = 7 + n 6x = 7 + n Divide each side by '6'. x = 1.166666667 + 0.1666666667n Simplifying x = 1.166666667 + 0.1666666667nSolution
x = {0, 1.166666667 + 0.1666666667n}
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