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Simplifying (x + 7)(x + -3) = (2x + 2)(x + -3) Reorder the terms: (7 + x)(x + -3) = (2x + 2)(x + -3) Reorder the terms: (7 + x)(-3 + x) = (2x + 2)(x + -3) Multiply (7 + x) * (-3 + x) (7(-3 + x) + x(-3 + x)) = (2x + 2)(x + -3) ((-3 * 7 + x * 7) + x(-3 + x)) = (2x + 2)(x + -3) ((-21 + 7x) + x(-3 + x)) = (2x + 2)(x + -3) (-21 + 7x + (-3 * x + x * x)) = (2x + 2)(x + -3) (-21 + 7x + (-3x + x2)) = (2x + 2)(x + -3) Combine like terms: 7x + -3x = 4x (-21 + 4x + x2) = (2x + 2)(x + -3) Reorder the terms: -21 + 4x + x2 = (2 + 2x)(x + -3) Reorder the terms: -21 + 4x + x2 = (2 + 2x)(-3 + x) Multiply (2 + 2x) * (-3 + x) -21 + 4x + x2 = (2(-3 + x) + 2x * (-3 + x)) -21 + 4x + x2 = ((-3 * 2 + x * 2) + 2x * (-3 + x)) -21 + 4x + x2 = ((-6 + 2x) + 2x * (-3 + x)) -21 + 4x + x2 = (-6 + 2x + (-3 * 2x + x * 2x)) -21 + 4x + x2 = (-6 + 2x + (-6x + 2x2)) Combine like terms: 2x + -6x = -4x -21 + 4x + x2 = (-6 + -4x + 2x2) Solving -21 + 4x + x2 = -6 + -4x + 2x2 Solving for variable 'x'. Reorder the terms: -21 + 6 + 4x + 4x + x2 + -2x2 = -6 + -4x + 2x2 + 6 + 4x + -2x2 Combine like terms: -21 + 6 = -15 -15 + 4x + 4x + x2 + -2x2 = -6 + -4x + 2x2 + 6 + 4x + -2x2 Combine like terms: 4x + 4x = 8x -15 + 8x + x2 + -2x2 = -6 + -4x + 2x2 + 6 + 4x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -15 + 8x + -1x2 = -6 + -4x + 2x2 + 6 + 4x + -2x2 Reorder the terms: -15 + 8x + -1x2 = -6 + 6 + -4x + 4x + 2x2 + -2x2 Combine like terms: -6 + 6 = 0 -15 + 8x + -1x2 = 0 + -4x + 4x + 2x2 + -2x2 -15 + 8x + -1x2 = -4x + 4x + 2x2 + -2x2 Combine like terms: -4x + 4x = 0 -15 + 8x + -1x2 = 0 + 2x2 + -2x2 -15 + 8x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -15 + 8x + -1x2 = 0 Factor a trinomial. (-5 + x)(3 + -1x) = 0Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 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 = {5, 3}
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