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Simplifying 0 = (12x2) + -42x + 36 Reorder the terms: 0 = 36 + -42x + (12x2) Solving 0 = 36 + -42x + (12x2) Solving for variable 'x'. Combine like terms: 0 + -36 = -36 -36 + 42x + (-12x2) = 36 + -42x + (12x2) + -36 + 42x + (-12x2) Reorder the terms: -36 + 42x + (-12x2) = 36 + -36 + -42x + 42x + (12x2) + (-12x2) Combine like terms: 36 + -36 = 0 -36 + 42x + (-12x2) = 0 + -42x + 42x + (12x2) + (-12x2) -36 + 42x + (-12x2) = -42x + 42x + (12x2) + (-12x2) Combine like terms: -42x + 42x = 0 -36 + 42x + (-12x2) = 0 + (12x2) + (-12x2) -36 + 42x + (-12x2) = (12x2) + (-12x2) Combine like terms: (12x2) + (-12x2) = 0 -36 + 42x + (-12x2) = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-6 + 7x + (-2x2)) = 0 Factor a trinomial. 6((-2 + x)(3 + -2x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 2
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 = 1.5Solution
x = {2, 1.5}
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