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Simplifying f(0) = -3x2 + -14x + 24 Reorder the terms for easier multiplication: 0f = -3x2 + -14x + 24 Anything times zero is zero. 0f = -3x2 + -14x + 24 Reorder the terms: 0 = 24 + -14x + -3x2 Solving 0 = 24 + -14x + -3x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + 14x + 3x2 = 24 + -14x + -3x2 + -24 + 14x + 3x2 Reorder the terms: -24 + 14x + 3x2 = 24 + -24 + -14x + 14x + -3x2 + 3x2 Combine like terms: 24 + -24 = 0 -24 + 14x + 3x2 = 0 + -14x + 14x + -3x2 + 3x2 -24 + 14x + 3x2 = -14x + 14x + -3x2 + 3x2 Combine like terms: -14x + 14x = 0 -24 + 14x + 3x2 = 0 + -3x2 + 3x2 -24 + 14x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -24 + 14x + 3x2 = 0 Factor a trinomial. (-6 + -1x)(4 + -3x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 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 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {-6, 1.333333333}
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