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Simplifying 0 = (3x + 11)((6x2) + 5x) Reorder the terms: 0 = (11 + 3x)((6x2) + 5x) Reorder the terms: 0 = (11 + 3x)(5x + (6x2)) Multiply (11 + 3x) * (5x + (6x2)) 0 = (11(5x + (6x2)) + 3x * (5x + (6x2))) 0 = ((5x * 11 + (6x2) * 11) + 3x * (5x + (6x2))) 0 = ((55x + 66x2) + 3x * (5x + (6x2))) 0 = (55x + 66x2 + (5x * 3x + (6x2) * 3x)) 0 = (55x + 66x2 + (15x2 + 18x3)) Combine like terms: 66x2 + 15x2 = 81x2 0 = (55x + 81x2 + 18x3) Solving 0 = 55x + 81x2 + 18x3 Solving for variable 'x'. Remove the zero: -55x + -81x2 + -18x3 = 55x + 81x2 + 18x3 + -55x + -81x2 + -18x3 Reorder the terms: -55x + -81x2 + -18x3 = 55x + -55x + 81x2 + -81x2 + 18x3 + -18x3 Combine like terms: 55x + -55x = 0 -55x + -81x2 + -18x3 = 0 + 81x2 + -81x2 + 18x3 + -18x3 -55x + -81x2 + -18x3 = 81x2 + -81x2 + 18x3 + -18x3 Combine like terms: 81x2 + -81x2 = 0 -55x + -81x2 + -18x3 = 0 + 18x3 + -18x3 -55x + -81x2 + -18x3 = 18x3 + -18x3 Combine like terms: 18x3 + -18x3 = 0 -55x + -81x2 + -18x3 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(55 + 81x + 18x2) = 0 Factor a trinomial. -1x((11 + 3x)(5 + 6x)) = 0 Ignore the factor -1.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 '(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 = -3.666666667Subproblem 3
Set the factor '(5 + 6x)' equal to zero and attempt to solve: Simplifying 5 + 6x = 0 Solving 5 + 6x = 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 + 6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6x = 0 + -5 6x = 0 + -5 Combine like terms: 0 + -5 = -5 6x = -5 Divide each side by '6'. x = -0.8333333333 Simplifying x = -0.8333333333Solution
x = {0, -3.666666667, -0.8333333333}
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