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Simplifying x(x + 2) * 2(x + 5) + x(x + 2) * 3 = 0 Reorder the terms: x(2 + x) * 2(x + 5) + x(x + 2) * 3 = 0 Reorder the terms: x(2 + x) * 2(5 + x) + x(x + 2) * 3 = 0 Reorder the terms for easier multiplication: 2x(2 + x)(5 + x) + x(x + 2) * 3 = 0 Multiply (2 + x) * (5 + x) 2x(2(5 + x) + x(5 + x)) + x(x + 2) * 3 = 0 2x((5 * 2 + x * 2) + x(5 + x)) + x(x + 2) * 3 = 0 2x((10 + 2x) + x(5 + x)) + x(x + 2) * 3 = 0 2x(10 + 2x + (5 * x + x * x)) + x(x + 2) * 3 = 0 2x(10 + 2x + (5x + x2)) + x(x + 2) * 3 = 0 Combine like terms: 2x + 5x = 7x 2x(10 + 7x + x2) + x(x + 2) * 3 = 0 (10 * 2x + 7x * 2x + x2 * 2x) + x(x + 2) * 3 = 0 (20x + 14x2 + 2x3) + x(x + 2) * 3 = 0 Reorder the terms: 20x + 14x2 + 2x3 + x(2 + x) * 3 = 0 Reorder the terms for easier multiplication: 20x + 14x2 + 2x3 + 3x(2 + x) = 0 20x + 14x2 + 2x3 + (2 * 3x + x * 3x) = 0 20x + 14x2 + 2x3 + (6x + 3x2) = 0 Reorder the terms: 20x + 6x + 14x2 + 3x2 + 2x3 = 0 Combine like terms: 20x + 6x = 26x 26x + 14x2 + 3x2 + 2x3 = 0 Combine like terms: 14x2 + 3x2 = 17x2 26x + 17x2 + 2x3 = 0 Solving 26x + 17x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(26 + 17x + 2x2) = 0 Factor a trinomial. x((13 + 2x)(2 + x)) = 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 '(13 + 2x)' equal to zero and attempt to solve: Simplifying 13 + 2x = 0 Solving 13 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 2x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 2x = 0 + -13 2x = 0 + -13 Combine like terms: 0 + -13 = -13 2x = -13 Divide each side by '2'. x = -6.5 Simplifying x = -6.5Subproblem 3
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 = {0, -6.5, -2}
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