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Simplifying 3x(x + -2) = (2x + 7)(x + -2) Reorder the terms: 3x(-2 + x) = (2x + 7)(x + -2) (-2 * 3x + x * 3x) = (2x + 7)(x + -2) (-6x + 3x2) = (2x + 7)(x + -2) Reorder the terms: -6x + 3x2 = (7 + 2x)(x + -2) Reorder the terms: -6x + 3x2 = (7 + 2x)(-2 + x) Multiply (7 + 2x) * (-2 + x) -6x + 3x2 = (7(-2 + x) + 2x * (-2 + x)) -6x + 3x2 = ((-2 * 7 + x * 7) + 2x * (-2 + x)) -6x + 3x2 = ((-14 + 7x) + 2x * (-2 + x)) -6x + 3x2 = (-14 + 7x + (-2 * 2x + x * 2x)) -6x + 3x2 = (-14 + 7x + (-4x + 2x2)) Combine like terms: 7x + -4x = 3x -6x + 3x2 = (-14 + 3x + 2x2) Solving -6x + 3x2 = -14 + 3x + 2x2 Solving for variable 'x'. Reorder the terms: 14 + -6x + -3x + 3x2 + -2x2 = -14 + 3x + 2x2 + 14 + -3x + -2x2 Combine like terms: -6x + -3x = -9x 14 + -9x + 3x2 + -2x2 = -14 + 3x + 2x2 + 14 + -3x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 14 + -9x + 1x2 = -14 + 3x + 2x2 + 14 + -3x + -2x2 Reorder the terms: 14 + -9x + 1x2 = -14 + 14 + 3x + -3x + 2x2 + -2x2 Combine like terms: -14 + 14 = 0 14 + -9x + 1x2 = 0 + 3x + -3x + 2x2 + -2x2 14 + -9x + 1x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 14 + -9x + 1x2 = 0 + 2x2 + -2x2 14 + -9x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 14 + -9x + 1x2 = 0 Factor a trinomial. (2 + -1x)(7 + -1x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {2, 7}
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