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Simplifying (3x + -1)(x2 + 5x) = 0 Reorder the terms: (-1 + 3x)(x2 + 5x) = 0 Reorder the terms: (-1 + 3x)(5x + x2) = 0 Multiply (-1 + 3x) * (5x + x2) (-1(5x + x2) + 3x * (5x + x2)) = 0 ((5x * -1 + x2 * -1) + 3x * (5x + x2)) = 0 ((-5x + -1x2) + 3x * (5x + x2)) = 0 (-5x + -1x2 + (5x * 3x + x2 * 3x)) = 0 (-5x + -1x2 + (15x2 + 3x3)) = 0 Combine like terms: -1x2 + 15x2 = 14x2 (-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((-5 + -1x)(1 + -3x)) = 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 '(-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 = -5Subproblem 3
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 = 0.3333333333Solution
x = {0, -5, 0.3333333333}
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