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Simplifying 6x2 = 21x + 12 Reorder the terms: 6x2 = 12 + 21x Solving 6x2 = 12 + 21x Solving for variable 'x'. Reorder the terms: -12 + -21x + 6x2 = 12 + 21x + -12 + -21x Reorder the terms: -12 + -21x + 6x2 = 12 + -12 + 21x + -21x Combine like terms: 12 + -12 = 0 -12 + -21x + 6x2 = 0 + 21x + -21x -12 + -21x + 6x2 = 21x + -21x Combine like terms: 21x + -21x = 0 -12 + -21x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + -7x + 2x2) = 0 Factor a trinomial. 3((-1 + -2x)(4 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-0.5, 4}
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