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Simplifying 0 = 6x2 + -30x + 24 Reorder the terms: 0 = 24 + -30x + 6x2 Solving 0 = 24 + -30x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + 30x + -6x2 = 24 + -30x + 6x2 + -24 + 30x + -6x2 Reorder the terms: -24 + 30x + -6x2 = 24 + -24 + -30x + 30x + 6x2 + -6x2 Combine like terms: 24 + -24 = 0 -24 + 30x + -6x2 = 0 + -30x + 30x + 6x2 + -6x2 -24 + 30x + -6x2 = -30x + 30x + 6x2 + -6x2 Combine like terms: -30x + 30x = 0 -24 + 30x + -6x2 = 0 + 6x2 + -6x2 -24 + 30x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -24 + 30x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + 5x + -1x2) = 0 Factor a trinomial. 6((-4 + x)(1 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 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 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 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 = {4, 1}
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