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Simplifying 0 = 6x2 + -24x + 18 Reorder the terms: 0 = 18 + -24x + 6x2 Solving 0 = 18 + -24x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -18 = -18 -18 + 24x + -6x2 = 18 + -24x + 6x2 + -18 + 24x + -6x2 Reorder the terms: -18 + 24x + -6x2 = 18 + -18 + -24x + 24x + 6x2 + -6x2 Combine like terms: 18 + -18 = 0 -18 + 24x + -6x2 = 0 + -24x + 24x + 6x2 + -6x2 -18 + 24x + -6x2 = -24x + 24x + 6x2 + -6x2 Combine like terms: -24x + 24x = 0 -18 + 24x + -6x2 = 0 + 6x2 + -6x2 -18 + 24x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -18 + 24x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + 4x + -1x2) = 0 Factor a trinomial. 6((-3 + x)(1 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
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 = 1Solution
x = {3, 1}
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