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Simplifying 0 = 3x2 + -21x + 30 Reorder the terms: 0 = 30 + -21x + 3x2 Solving 0 = 30 + -21x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -30 = -30 -30 + 21x + -3x2 = 30 + -21x + 3x2 + -30 + 21x + -3x2 Reorder the terms: -30 + 21x + -3x2 = 30 + -30 + -21x + 21x + 3x2 + -3x2 Combine like terms: 30 + -30 = 0 -30 + 21x + -3x2 = 0 + -21x + 21x + 3x2 + -3x2 -30 + 21x + -3x2 = -21x + 21x + 3x2 + -3x2 Combine like terms: -21x + 21x = 0 -30 + 21x + -3x2 = 0 + 3x2 + -3x2 -30 + 21x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -30 + 21x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + 7x + -1x2) = 0 Factor a trinomial. 3((-5 + x)(2 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {5, 2}
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