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Simplifying (x + 4)(x + -7) = (2x + 5)(x + -7) Reorder the terms: (4 + x)(x + -7) = (2x + 5)(x + -7) Reorder the terms: (4 + x)(-7 + x) = (2x + 5)(x + -7) Multiply (4 + x) * (-7 + x) (4(-7 + x) + x(-7 + x)) = (2x + 5)(x + -7) ((-7 * 4 + x * 4) + x(-7 + x)) = (2x + 5)(x + -7) ((-28 + 4x) + x(-7 + x)) = (2x + 5)(x + -7) (-28 + 4x + (-7 * x + x * x)) = (2x + 5)(x + -7) (-28 + 4x + (-7x + x2)) = (2x + 5)(x + -7) Combine like terms: 4x + -7x = -3x (-28 + -3x + x2) = (2x + 5)(x + -7) Reorder the terms: -28 + -3x + x2 = (5 + 2x)(x + -7) Reorder the terms: -28 + -3x + x2 = (5 + 2x)(-7 + x) Multiply (5 + 2x) * (-7 + x) -28 + -3x + x2 = (5(-7 + x) + 2x * (-7 + x)) -28 + -3x + x2 = ((-7 * 5 + x * 5) + 2x * (-7 + x)) -28 + -3x + x2 = ((-35 + 5x) + 2x * (-7 + x)) -28 + -3x + x2 = (-35 + 5x + (-7 * 2x + x * 2x)) -28 + -3x + x2 = (-35 + 5x + (-14x + 2x2)) Combine like terms: 5x + -14x = -9x -28 + -3x + x2 = (-35 + -9x + 2x2) Solving -28 + -3x + x2 = -35 + -9x + 2x2 Solving for variable 'x'. Reorder the terms: -28 + 35 + -3x + 9x + x2 + -2x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2 Combine like terms: -28 + 35 = 7 7 + -3x + 9x + x2 + -2x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2 Combine like terms: -3x + 9x = 6x 7 + 6x + x2 + -2x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2 Combine like terms: x2 + -2x2 = -1x2 7 + 6x + -1x2 = -35 + -9x + 2x2 + 35 + 9x + -2x2 Reorder the terms: 7 + 6x + -1x2 = -35 + 35 + -9x + 9x + 2x2 + -2x2 Combine like terms: -35 + 35 = 0 7 + 6x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2 7 + 6x + -1x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 7 + 6x + -1x2 = 0 + 2x2 + -2x2 7 + 6x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 7 + 6x + -1x2 = 0 Factor a trinomial. (7 + -1x)(1 + 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {7, -1}
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