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Simplifying 0 = 75x3 + 90x2 + 27x Reorder the terms: 0 = 27x + 90x2 + 75x3 Solving 0 = 27x + 90x2 + 75x3 Solving for variable 'x'. Remove the zero: -27x + -90x2 + -75x3 = 27x + 90x2 + 75x3 + -27x + -90x2 + -75x3 Reorder the terms: -27x + -90x2 + -75x3 = 27x + -27x + 90x2 + -90x2 + 75x3 + -75x3 Combine like terms: 27x + -27x = 0 -27x + -90x2 + -75x3 = 0 + 90x2 + -90x2 + 75x3 + -75x3 -27x + -90x2 + -75x3 = 90x2 + -90x2 + 75x3 + -75x3 Combine like terms: 90x2 + -90x2 = 0 -27x + -90x2 + -75x3 = 0 + 75x3 + -75x3 -27x + -90x2 + -75x3 = 75x3 + -75x3 Combine like terms: 75x3 + -75x3 = 0 -27x + -90x2 + -75x3 = 0 Factor out the Greatest Common Factor (GCF), '-3x'. -3x(9 + 30x + 25x2) = 0 Factor a trinomial. -3x((3 + 5x)(3 + 5x)) = 0 Ignore the factor -3.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 '(3 + 5x)' equal to zero and attempt to solve: Simplifying 3 + 5x = 0 Solving 3 + 5x = 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 + 5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x = 0 + -3 5x = 0 + -3 Combine like terms: 0 + -3 = -3 5x = -3 Divide each side by '5'. x = -0.6 Simplifying x = -0.6Subproblem 3
Set the factor '(3 + 5x)' equal to zero and attempt to solve: Simplifying 3 + 5x = 0 Solving 3 + 5x = 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 + 5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x = 0 + -3 5x = 0 + -3 Combine like terms: 0 + -3 = -3 5x = -3 Divide each side by '5'. x = -0.6 Simplifying x = -0.6Solution
x = {0, -0.6, -0.6}
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