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Simplifying (2x + 5)(4p + 4)(3x + 3) = 0 Reorder the terms: (5 + 2x)(4p + 4)(3x + 3) = 0 Reorder the terms: (5 + 2x)(4 + 4p)(3x + 3) = 0 Reorder the terms: (5 + 2x)(4 + 4p)(3 + 3x) = 0 Multiply (5 + 2x) * (4 + 4p) (5(4 + 4p) + 2x * (4 + 4p))(3 + 3x) = 0 ((4 * 5 + 4p * 5) + 2x * (4 + 4p))(3 + 3x) = 0 ((20 + 20p) + 2x * (4 + 4p))(3 + 3x) = 0 (20 + 20p + (4 * 2x + 4p * 2x))(3 + 3x) = 0 Reorder the terms: (20 + 20p + (8px + 8x))(3 + 3x) = 0 (20 + 20p + (8px + 8x))(3 + 3x) = 0 (20 + 20p + 8px + 8x)(3 + 3x) = 0 Multiply (20 + 20p + 8px + 8x) * (3 + 3x) (20(3 + 3x) + 20p * (3 + 3x) + 8px * (3 + 3x) + 8x * (3 + 3x)) = 0 ((3 * 20 + 3x * 20) + 20p * (3 + 3x) + 8px * (3 + 3x) + 8x * (3 + 3x)) = 0 ((60 + 60x) + 20p * (3 + 3x) + 8px * (3 + 3x) + 8x * (3 + 3x)) = 0 (60 + 60x + (3 * 20p + 3x * 20p) + 8px * (3 + 3x) + 8x * (3 + 3x)) = 0 (60 + 60x + (60p + 60px) + 8px * (3 + 3x) + 8x * (3 + 3x)) = 0 (60 + 60x + 60p + 60px + (3 * 8px + 3x * 8px) + 8x * (3 + 3x)) = 0 (60 + 60x + 60p + 60px + (24px + 24px2) + 8x * (3 + 3x)) = 0 (60 + 60x + 60p + 60px + 24px + 24px2 + (3 * 8x + 3x * 8x)) = 0 (60 + 60x + 60p + 60px + 24px + 24px2 + (24x + 24x2)) = 0 Reorder the terms: (60 + 60p + 60px + 24px + 24px2 + 60x + 24x + 24x2) = 0 Combine like terms: 60px + 24px = 84px (60 + 60p + 84px + 24px2 + 60x + 24x + 24x2) = 0 Combine like terms: 60x + 24x = 84x (60 + 60p + 84px + 24px2 + 84x + 24x2) = 0 Solving 60 + 60p + 84px + 24px2 + 84x + 24x2 = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + 60p + 84px + 24px2 + 84x + -60 + 24x2 = 0 + -60 Reorder the terms: 60 + -60 + 60p + 84px + 24px2 + 84x + 24x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 60p + 84px + 24px2 + 84x + 24x2 = 0 + -60 60p + 84px + 24px2 + 84x + 24x2 = 0 + -60 Combine like terms: 0 + -60 = -60 60p + 84px + 24px2 + 84x + 24x2 = -60 Add '-84x' to each side of the equation. 60p + 84px + 24px2 + 84x + -84x + 24x2 = -60 + -84x Combine like terms: 84x + -84x = 0 60p + 84px + 24px2 + 0 + 24x2 = -60 + -84x 60p + 84px + 24px2 + 24x2 = -60 + -84x Add '-24x2' to each side of the equation. 60p + 84px + 24px2 + 24x2 + -24x2 = -60 + -84x + -24x2 Combine like terms: 24x2 + -24x2 = 0 60p + 84px + 24px2 + 0 = -60 + -84x + -24x2 60p + 84px + 24px2 = -60 + -84x + -24x2 Reorder the terms: 60 + 60p + 84px + 24px2 + 84x + 24x2 = -60 + -84x + -24x2 + 60 + 84x + 24x2 Reorder the terms: 60 + 60p + 84px + 24px2 + 84x + 24x2 = -60 + 60 + -84x + 84x + -24x2 + 24x2 Combine like terms: -60 + 60 = 0 60 + 60p + 84px + 24px2 + 84x + 24x2 = 0 + -84x + 84x + -24x2 + 24x2 60 + 60p + 84px + 24px2 + 84x + 24x2 = -84x + 84x + -24x2 + 24x2 Combine like terms: -84x + 84x = 0 60 + 60p + 84px + 24px2 + 84x + 24x2 = 0 + -24x2 + 24x2 60 + 60p + 84px + 24px2 + 84x + 24x2 = -24x2 + 24x2 Combine like terms: -24x2 + 24x2 = 0 60 + 60p + 84px + 24px2 + 84x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(5 + 5p + 7px + 2px2 + 7x + 2x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(5 + 5p + 7px + 2px2 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 5p + 7px + 2px2 + 7x + 2x2 = 0 Solving 5 + 5p + 7px + 2px2 + 7x + 2x2 = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 5p + 7px + 2px2 + 7x + -5 + 2x2 = 0 + -5 Reorder the terms: 5 + -5 + 5p + 7px + 2px2 + 7x + 2x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5p + 7px + 2px2 + 7x + 2x2 = 0 + -5 5p + 7px + 2px2 + 7x + 2x2 = 0 + -5 Combine like terms: 0 + -5 = -5 5p + 7px + 2px2 + 7x + 2x2 = -5 Add '-7x' to each side of the equation. 5p + 7px + 2px2 + 7x + -7x + 2x2 = -5 + -7x Combine like terms: 7x + -7x = 0 5p + 7px + 2px2 + 0 + 2x2 = -5 + -7x 5p + 7px + 2px2 + 2x2 = -5 + -7x Add '-2x2' to each side of the equation. 5p + 7px + 2px2 + 2x2 + -2x2 = -5 + -7x + -2x2 Combine like terms: 2x2 + -2x2 = 0 5p + 7px + 2px2 + 0 = -5 + -7x + -2x2 5p + 7px + 2px2 = -5 + -7x + -2x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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