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Simplifying 10x3 + 12x = -23x2 Reorder the terms: 12x + 10x3 = -23x2 Solving 12x + 10x3 = -23x2 Solving for variable 'x'. Reorder the terms: 12x + 23x2 + 10x3 = -23x2 + 23x2 Combine like terms: -23x2 + 23x2 = 0 12x + 23x2 + 10x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(12 + 23x + 10x2) = 0 Factor a trinomial. x((3 + 2x)(4 + 5x)) = 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 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 3
Set the factor '(4 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Divide each side by '5'. x = -0.8 Simplifying x = -0.8Solution
x = {0, -1.5, -0.8}
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