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Simplifying 0 = 5 + 2x + -3x2 Solving 0 = 5 + 2x + -3x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -2x + 3x2 = 5 + 2x + -3x2 + -5 + -2x + 3x2 Reorder the terms: -5 + -2x + 3x2 = 5 + -5 + 2x + -2x + -3x2 + 3x2 Combine like terms: 5 + -5 = 0 -5 + -2x + 3x2 = 0 + 2x + -2x + -3x2 + 3x2 -5 + -2x + 3x2 = 2x + -2x + -3x2 + 3x2 Combine like terms: 2x + -2x = 0 -5 + -2x + 3x2 = 0 + -3x2 + 3x2 -5 + -2x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -5 + -2x + 3x2 = 0 Factor a trinomial. (-1 + -1x)(5 + -3x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
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 = {-1, 1.666666667}
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