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Simplifying (x + 8)(x + 7)(x + 0)(x + -8)(x + -7) = 0 Reorder the terms: (8 + x)(x + 7)(x + 0)(x + -8)(x + -7) = 0 Reorder the terms: (8 + x)(7 + x)(x + 0)(x + -8)(x + -7) = 0 Reorder the terms: (8 + x)(7 + x)(0 + x)(x + -8)(x + -7) = 0 Remove the zero: (8 + x)(7 + x)(x)(x + -8)(x + -7) = 0 Reorder the terms: (8 + x)(7 + x) * x(-8 + x)(x + -7) = 0 Reorder the terms: (8 + x)(7 + x) * x(-8 + x)(-7 + x) = 0 Reorder the terms for easier multiplication: x(8 + x)(7 + x)(-8 + x)(-7 + x) = 0 Multiply (8 + x) * (7 + x) x(8(7 + x) + x(7 + x))(-8 + x)(-7 + x) = 0 x((7 * 8 + x * 8) + x(7 + x))(-8 + x)(-7 + x) = 0 x((56 + 8x) + x(7 + x))(-8 + x)(-7 + x) = 0 x(56 + 8x + (7 * x + x * x))(-8 + x)(-7 + x) = 0 x(56 + 8x + (7x + x2))(-8 + x)(-7 + x) = 0 Combine like terms: 8x + 7x = 15x x(56 + 15x + x2)(-8 + x)(-7 + x) = 0 Multiply (56 + 15x + x2) * (-8 + x) x(56(-8 + x) + 15x * (-8 + x) + x2(-8 + x))(-7 + x) = 0 x((-8 * 56 + x * 56) + 15x * (-8 + x) + x2(-8 + x))(-7 + x) = 0 x((-448 + 56x) + 15x * (-8 + x) + x2(-8 + x))(-7 + x) = 0 x(-448 + 56x + (-8 * 15x + x * 15x) + x2(-8 + x))(-7 + x) = 0 x(-448 + 56x + (-120x + 15x2) + x2(-8 + x))(-7 + x) = 0 x(-448 + 56x + -120x + 15x2 + (-8 * x2 + x * x2))(-7 + x) = 0 x(-448 + 56x + -120x + 15x2 + (-8x2 + x3))(-7 + x) = 0 Combine like terms: 56x + -120x = -64x x(-448 + -64x + 15x2 + -8x2 + x3)(-7 + x) = 0 Combine like terms: 15x2 + -8x2 = 7x2 x(-448 + -64x + 7x2 + x3)(-7 + x) = 0 Multiply (-448 + -64x + 7x2 + x3) * (-7 + x) x(-448(-7 + x) + -64x * (-7 + x) + 7x2 * (-7 + x) + x3(-7 + x)) = 0 x((-7 * -448 + x * -448) + -64x * (-7 + x) + 7x2 * (-7 + x) + x3(-7 + x)) = 0 x((3136 + -448x) + -64x * (-7 + x) + 7x2 * (-7 + x) + x3(-7 + x)) = 0 x(3136 + -448x + (-7 * -64x + x * -64x) + 7x2 * (-7 + x) + x3(-7 + x)) = 0 x(3136 + -448x + (448x + -64x2) + 7x2 * (-7 + x) + x3(-7 + x)) = 0 x(3136 + -448x + 448x + -64x2 + (-7 * 7x2 + x * 7x2) + x3(-7 + x)) = 0 x(3136 + -448x + 448x + -64x2 + (-49x2 + 7x3) + x3(-7 + x)) = 0 x(3136 + -448x + 448x + -64x2 + -49x2 + 7x3 + (-7 * x3 + x * x3)) = 0 x(3136 + -448x + 448x + -64x2 + -49x2 + 7x3 + (-7x3 + x4)) = 0 Combine like terms: -448x + 448x = 0 x(3136 + 0 + -64x2 + -49x2 + 7x3 + -7x3 + x4) = 0 x(3136 + -64x2 + -49x2 + 7x3 + -7x3 + x4) = 0 Combine like terms: -64x2 + -49x2 = -113x2 x(3136 + -113x2 + 7x3 + -7x3 + x4) = 0 Combine like terms: 7x3 + -7x3 = 0 x(3136 + -113x2 + 0 + x4) = 0 x(3136 + -113x2 + x4) = 0 (3136 * x + -113x2 * x + x4 * x) = 0 (3136x + -113x3 + x5) = 0 Solving 3136x + -113x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3136 + -113x2 + x4) = 0 Factor a trinomial. x((49 + -1x2)(64 + -1x2)) = 0 Factor a difference between two squares. x(((7 + x)(7 + -1x))(64 + -1x2)) = 0 Factor a difference between two squares. x(((8 + x)(8 + -1x))(7 + x)(7 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 3
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 4
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Subproblem 5
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {0, -7, 7, -8, 8}
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