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Simplifying F(0) = 12x2 + 8x + -15 Reorder the terms for easier multiplication: 0F = 12x2 + 8x + -15 Anything times zero is zero. 0F = 12x2 + 8x + -15 Reorder the terms: 0 = -15 + 8x + 12x2 Solving 0 = -15 + 8x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 15 = 15 15 + -8x + -12x2 = -15 + 8x + 12x2 + 15 + -8x + -12x2 Reorder the terms: 15 + -8x + -12x2 = -15 + 15 + 8x + -8x + 12x2 + -12x2 Combine like terms: -15 + 15 = 0 15 + -8x + -12x2 = 0 + 8x + -8x + 12x2 + -12x2 15 + -8x + -12x2 = 8x + -8x + 12x2 + -12x2 Combine like terms: 8x + -8x = 0 15 + -8x + -12x2 = 0 + 12x2 + -12x2 15 + -8x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 15 + -8x + -12x2 = 0 Factor a trinomial. (5 + -6x)(3 + 2x) = 0Subproblem 1
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 = 0.8333333333Subproblem 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 = -1.5Solution
x = {0.8333333333, -1.5}
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