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Simplifying (x + 3)(3x2 + 5x) = 0 Reorder the terms: (3 + x)(3x2 + 5x) = 0 Reorder the terms: (3 + x)(5x + 3x2) = 0 Multiply (3 + x) * (5x + 3x2) (3(5x + 3x2) + x(5x + 3x2)) = 0 ((5x * 3 + 3x2 * 3) + x(5x + 3x2)) = 0 ((15x + 9x2) + x(5x + 3x2)) = 0 (15x + 9x2 + (5x * x + 3x2 * x)) = 0 (15x + 9x2 + (5x2 + 3x3)) = 0 Combine like terms: 9x2 + 5x2 = 14x2 (15x + 14x2 + 3x3) = 0 Solving 15x + 14x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(15 + 14x + 3x2) = 0 Factor a trinomial. x((3 + x)(5 + 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 3
Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 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 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Solution
x = {0, -3, -1.666666667}
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