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Simplifying (x + -5) * x(x + 2) + -1(1 + -2x) * x(x + -5) = 0 Reorder the terms: (-5 + x) * x(x + 2) + -1(1 + -2x) * x(x + -5) = 0 Reorder the terms: (-5 + x) * x(2 + x) + -1(1 + -2x) * x(x + -5) = 0 Reorder the terms for easier multiplication: x(-5 + x)(2 + x) + -1(1 + -2x) * x(x + -5) = 0 Multiply (-5 + x) * (2 + x) x(-5(2 + x) + x(2 + x)) + -1(1 + -2x) * x(x + -5) = 0 x((2 * -5 + x * -5) + x(2 + x)) + -1(1 + -2x) * x(x + -5) = 0 x((-10 + -5x) + x(2 + x)) + -1(1 + -2x) * x(x + -5) = 0 x(-10 + -5x + (2 * x + x * x)) + -1(1 + -2x) * x(x + -5) = 0 x(-10 + -5x + (2x + x2)) + -1(1 + -2x) * x(x + -5) = 0 Combine like terms: -5x + 2x = -3x x(-10 + -3x + x2) + -1(1 + -2x) * x(x + -5) = 0 (-10 * x + -3x * x + x2 * x) + -1(1 + -2x) * x(x + -5) = 0 (-10x + -3x2 + x3) + -1(1 + -2x) * x(x + -5) = 0 Reorder the terms: -10x + -3x2 + x3 + -1(1 + -2x) * x(-5 + x) = 0 Reorder the terms for easier multiplication: -10x + -3x2 + x3 + -1x(1 + -2x)(-5 + x) = 0 Multiply (1 + -2x) * (-5 + x) -10x + -3x2 + x3 + -1x(1(-5 + x) + -2x * (-5 + x)) = 0 -10x + -3x2 + x3 + -1x((-5 * 1 + x * 1) + -2x * (-5 + x)) = 0 -10x + -3x2 + x3 + -1x((-5 + 1x) + -2x * (-5 + x)) = 0 -10x + -3x2 + x3 + -1x(-5 + 1x + (-5 * -2x + x * -2x)) = 0 -10x + -3x2 + x3 + -1x(-5 + 1x + (10x + -2x2)) = 0 Combine like terms: 1x + 10x = 11x -10x + -3x2 + x3 + -1x(-5 + 11x + -2x2) = 0 -10x + -3x2 + x3 + (-5 * -1x + 11x * -1x + -2x2 * -1x) = 0 -10x + -3x2 + x3 + (5x + -11x2 + 2x3) = 0 Reorder the terms: -10x + 5x + -3x2 + -11x2 + x3 + 2x3 = 0 Combine like terms: -10x + 5x = -5x -5x + -3x2 + -11x2 + x3 + 2x3 = 0 Combine like terms: -3x2 + -11x2 = -14x2 -5x + -14x2 + x3 + 2x3 = 0 Combine like terms: x3 + 2x3 = 3x3 -5x + -14x2 + 3x3 = 0 Solving -5x + -14x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + -14x + 3x2) = 0 Factor a trinomial. x((-1 + -3x)(5 + -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 '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, -0.3333333333, 5}
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