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Simplifying 0 = 6x2 + -17x + 12 Reorder the terms: 0 = 12 + -17x + 6x2 Solving 0 = 12 + -17x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + 17x + -6x2 = 12 + -17x + 6x2 + -12 + 17x + -6x2 Reorder the terms: -12 + 17x + -6x2 = 12 + -12 + -17x + 17x + 6x2 + -6x2 Combine like terms: 12 + -12 = 0 -12 + 17x + -6x2 = 0 + -17x + 17x + 6x2 + -6x2 -12 + 17x + -6x2 = -17x + 17x + 6x2 + -6x2 Combine like terms: -17x + 17x = 0 -12 + 17x + -6x2 = 0 + 6x2 + -6x2 -12 + 17x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -12 + 17x + -6x2 = 0 Factor a trinomial. (-3 + 2x)(4 + -3x) = 0Subproblem 1
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 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 = {1.5, 1.333333333}
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