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Simplifying (-3 + x)(x + 7) = (x + -3)(2x + 1) Reorder the terms: (-3 + x)(7 + x) = (x + -3)(2x + 1) Multiply (-3 + x) * (7 + x) (-3(7 + x) + x(7 + x)) = (x + -3)(2x + 1) ((7 * -3 + x * -3) + x(7 + x)) = (x + -3)(2x + 1) ((-21 + -3x) + x(7 + x)) = (x + -3)(2x + 1) (-21 + -3x + (7 * x + x * x)) = (x + -3)(2x + 1) (-21 + -3x + (7x + x2)) = (x + -3)(2x + 1) Combine like terms: -3x + 7x = 4x (-21 + 4x + x2) = (x + -3)(2x + 1) Reorder the terms: -21 + 4x + x2 = (-3 + x)(2x + 1) Reorder the terms: -21 + 4x + x2 = (-3 + x)(1 + 2x) Multiply (-3 + x) * (1 + 2x) -21 + 4x + x2 = (-3(1 + 2x) + x(1 + 2x)) -21 + 4x + x2 = ((1 * -3 + 2x * -3) + x(1 + 2x)) -21 + 4x + x2 = ((-3 + -6x) + x(1 + 2x)) -21 + 4x + x2 = (-3 + -6x + (1 * x + 2x * x)) -21 + 4x + x2 = (-3 + -6x + (1x + 2x2)) Combine like terms: -6x + 1x = -5x -21 + 4x + x2 = (-3 + -5x + 2x2) Solving -21 + 4x + x2 = -3 + -5x + 2x2 Solving for variable 'x'. Reorder the terms: -21 + 3 + 4x + 5x + x2 + -2x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2 Combine like terms: -21 + 3 = -18 -18 + 4x + 5x + x2 + -2x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2 Combine like terms: 4x + 5x = 9x -18 + 9x + x2 + -2x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -18 + 9x + -1x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2 Reorder the terms: -18 + 9x + -1x2 = -3 + 3 + -5x + 5x + 2x2 + -2x2 Combine like terms: -3 + 3 = 0 -18 + 9x + -1x2 = 0 + -5x + 5x + 2x2 + -2x2 -18 + 9x + -1x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 -18 + 9x + -1x2 = 0 + 2x2 + -2x2 -18 + 9x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -18 + 9x + -1x2 = 0 Factor a trinomial. (-6 + x)(3 + -1x) = 0Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {6, 3}
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