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Simplifying (x + 3)(x + -7) = (2x + 5)(x + -7) Reorder the terms: (3 + x)(x + -7) = (2x + 5)(x + -7) Reorder the terms: (3 + x)(-7 + x) = (2x + 5)(x + -7) Multiply (3 + x) * (-7 + x) (3(-7 + x) + x(-7 + x)) = (2x + 5)(x + -7) ((-7 * 3 + x * 3) + x(-7 + x)) = (2x + 5)(x + -7) ((-21 + 3x) + x(-7 + x)) = (2x + 5)(x + -7) (-21 + 3x + (-7 * x + x * x)) = (2x + 5)(x + -7) (-21 + 3x + (-7x + x2)) = (2x + 5)(x + -7) Combine like terms: 3x + -7x = -4x (-21 + -4x + x2) = (2x + 5)(x + -7) Reorder the terms: -21 + -4x + x2 = (5 + 2x)(x + -7) Reorder the terms: -21 + -4x + x2 = (5 + 2x)(-7 + x) Multiply (5 + 2x) * (-7 + x) -21 + -4x + x2 = (5(-7 + x) + 2x * (-7 + x)) -21 + -4x + x2 = ((-7 * 5 + x * 5) + 2x * (-7 + x)) -21 + -4x + x2 = ((-35 + 5x) + 2x * (-7 + x)) -21 + -4x + x2 = (-35 + 5x + (-7 * 2x + x * 2x)) -21 + -4x + x2 = (-35 + 5x + (-14x + 2x2)) Combine like terms: 5x + -14x = -9x -21 + -4x + x2 = (-35 + -9x + 2x2) Solving -21 + -4x + x2 = -35 + -9x + 2x2 Solving for variable 'x'. Reorder the terms: -21 + 35 + -4x + 9x + x2 + -2x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2 Combine like terms: -21 + 35 = 14 14 + -4x + 9x + x2 + -2x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2 Combine like terms: -4x + 9x = 5x 14 + 5x + x2 + -2x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2 Combine like terms: x2 + -2x2 = -1x2 14 + 5x + -1x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2 Reorder the terms: 14 + 5x + -1x2 = -35 + 35 + -9x + 9x + 2x2 + -2x2 Combine like terms: -35 + 35 = 0 14 + 5x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2 14 + 5x + -1x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 14 + 5x + -1x2 = 0 + 2x2 + -2x2 14 + 5x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 14 + 5x + -1x2 = 0 Factor a trinomial. (7 + -1x)(2 + x) = 0Subproblem 1
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 = 7Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {7, -2}
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