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Simplifying 9x(x + -6) = (2x + 1)(x + -6) Reorder the terms: 9x(-6 + x) = (2x + 1)(x + -6) (-6 * 9x + x * 9x) = (2x + 1)(x + -6) (-54x + 9x2) = (2x + 1)(x + -6) Reorder the terms: -54x + 9x2 = (1 + 2x)(x + -6) Reorder the terms: -54x + 9x2 = (1 + 2x)(-6 + x) Multiply (1 + 2x) * (-6 + x) -54x + 9x2 = (1(-6 + x) + 2x * (-6 + x)) -54x + 9x2 = ((-6 * 1 + x * 1) + 2x * (-6 + x)) -54x + 9x2 = ((-6 + 1x) + 2x * (-6 + x)) -54x + 9x2 = (-6 + 1x + (-6 * 2x + x * 2x)) -54x + 9x2 = (-6 + 1x + (-12x + 2x2)) Combine like terms: 1x + -12x = -11x -54x + 9x2 = (-6 + -11x + 2x2) Solving -54x + 9x2 = -6 + -11x + 2x2 Solving for variable 'x'. Reorder the terms: 6 + -54x + 11x + 9x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Combine like terms: -54x + 11x = -43x 6 + -43x + 9x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Combine like terms: 9x2 + -2x2 = 7x2 6 + -43x + 7x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2 Reorder the terms: 6 + -43x + 7x2 = -6 + 6 + -11x + 11x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 6 + -43x + 7x2 = 0 + -11x + 11x + 2x2 + -2x2 6 + -43x + 7x2 = -11x + 11x + 2x2 + -2x2 Combine like terms: -11x + 11x = 0 6 + -43x + 7x2 = 0 + 2x2 + -2x2 6 + -43x + 7x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 6 + -43x + 7x2 = 0 Factor a trinomial. (1 + -7x)(6 + -1x) = 0Subproblem 1
Set the factor '(1 + -7x)' equal to zero and attempt to solve: Simplifying 1 + -7x = 0 Solving 1 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7x = 0 + -1 -7x = 0 + -1 Combine like terms: 0 + -1 = -1 -7x = -1 Divide each side by '-7'. x = 0.1428571429 Simplifying x = 0.1428571429Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0.1428571429, 6}
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