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Simplifying (x + 3)(x + -3) = (2x + 7)(x + -3) Reorder the terms: (3 + x)(x + -3) = (2x + 7)(x + -3) Reorder the terms: (3 + x)(-3 + x) = (2x + 7)(x + -3) Multiply (3 + x) * (-3 + x) (3(-3 + x) + x(-3 + x)) = (2x + 7)(x + -3) ((-3 * 3 + x * 3) + x(-3 + x)) = (2x + 7)(x + -3) ((-9 + 3x) + x(-3 + x)) = (2x + 7)(x + -3) (-9 + 3x + (-3 * x + x * x)) = (2x + 7)(x + -3) (-9 + 3x + (-3x + x2)) = (2x + 7)(x + -3) Combine like terms: 3x + -3x = 0 (-9 + 0 + x2) = (2x + 7)(x + -3) (-9 + x2) = (2x + 7)(x + -3) Reorder the terms: -9 + x2 = (7 + 2x)(x + -3) Reorder the terms: -9 + x2 = (7 + 2x)(-3 + x) Multiply (7 + 2x) * (-3 + x) -9 + x2 = (7(-3 + x) + 2x * (-3 + x)) -9 + x2 = ((-3 * 7 + x * 7) + 2x * (-3 + x)) -9 + x2 = ((-21 + 7x) + 2x * (-3 + x)) -9 + x2 = (-21 + 7x + (-3 * 2x + x * 2x)) -9 + x2 = (-21 + 7x + (-6x + 2x2)) Combine like terms: 7x + -6x = 1x -9 + x2 = (-21 + 1x + 2x2) Solving -9 + x2 = -21 + 1x + 2x2 Solving for variable 'x'. Reorder the terms: -9 + 21 + -1x + x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2 Combine like terms: -9 + 21 = 12 12 + -1x + x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2 Combine like terms: x2 + -2x2 = -1x2 12 + -1x + -1x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2 Reorder the terms: 12 + -1x + -1x2 = -21 + 21 + 1x + -1x + 2x2 + -2x2 Combine like terms: -21 + 21 = 0 12 + -1x + -1x2 = 0 + 1x + -1x + 2x2 + -2x2 12 + -1x + -1x2 = 1x + -1x + 2x2 + -2x2 Combine like terms: 1x + -1x = 0 12 + -1x + -1x2 = 0 + 2x2 + -2x2 12 + -1x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 12 + -1x + -1x2 = 0 Factor a trinomial. (3 + -1x)(4 + x) = 0Subproblem 1
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 = 3Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {3, -4}
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