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Simplifying 0 = 5x(2x + 9)(3x + 11) Reorder the terms: 0 = 5x(9 + 2x)(3x + 11) Reorder the terms: 0 = 5x(9 + 2x)(11 + 3x) Multiply (9 + 2x) * (11 + 3x) 0 = 5x(9(11 + 3x) + 2x * (11 + 3x)) 0 = 5x((11 * 9 + 3x * 9) + 2x * (11 + 3x)) 0 = 5x((99 + 27x) + 2x * (11 + 3x)) 0 = 5x(99 + 27x + (11 * 2x + 3x * 2x)) 0 = 5x(99 + 27x + (22x + 6x2)) Combine like terms: 27x + 22x = 49x 0 = 5x(99 + 49x + 6x2) 0 = (99 * 5x + 49x * 5x + 6x2 * 5x) 0 = (495x + 245x2 + 30x3) Solving 0 = 495x + 245x2 + 30x3 Solving for variable 'x'. Remove the zero: -495x + -245x2 + -30x3 = 495x + 245x2 + 30x3 + -495x + -245x2 + -30x3 Reorder the terms: -495x + -245x2 + -30x3 = 495x + -495x + 245x2 + -245x2 + 30x3 + -30x3 Combine like terms: 495x + -495x = 0 -495x + -245x2 + -30x3 = 0 + 245x2 + -245x2 + 30x3 + -30x3 -495x + -245x2 + -30x3 = 245x2 + -245x2 + 30x3 + -30x3 Combine like terms: 245x2 + -245x2 = 0 -495x + -245x2 + -30x3 = 0 + 30x3 + -30x3 -495x + -245x2 + -30x3 = 30x3 + -30x3 Combine like terms: 30x3 + -30x3 = 0 -495x + -245x2 + -30x3 = 0 Factor out the Greatest Common Factor (GCF), '-5x'. -5x(99 + 49x + 6x2) = 0 Factor a trinomial. -5x((9 + 2x)(11 + 3x)) = 0 Ignore the factor -5.Subproblem 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 '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5Subproblem 3
Set the factor '(11 + 3x)' equal to zero and attempt to solve: Simplifying 11 + 3x = 0 Solving 11 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 3x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 3x = 0 + -11 3x = 0 + -11 Combine like terms: 0 + -11 = -11 3x = -11 Divide each side by '3'. x = -3.666666667 Simplifying x = -3.666666667Solution
x = {0, -4.5, -3.666666667}
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