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Simplifying 84x2 + 218x + -32 = 6x Reorder the terms: -32 + 218x + 84x2 = 6x Solving -32 + 218x + 84x2 = 6x Solving for variable 'x'. Reorder the terms: -32 + 218x + -6x + 84x2 = 6x + -6x Combine like terms: 218x + -6x = 212x -32 + 212x + 84x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -32 + 212x + 84x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-8 + 53x + 21x2) = 0 Factor a trinomial. 4((-8 + -3x)(1 + -7x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve: Simplifying -8 + -3x = 0 Solving -8 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3x = 0 + 8 -3x = 0 + 8 Combine like terms: 0 + 8 = 8 -3x = 8 Divide each side by '-3'. x = -2.666666667 Simplifying x = -2.666666667Subproblem 2
Set the factor '(1 + -7x)' equal to zero and attempt to solve: Simplifying 1 + -7x = 0 Solving 1 + -7x = 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 + -7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7x = 0 + -1 -7x = 0 + -1 Combine like terms: 0 + -1 = -1 -7x = -1 Divide each side by '-7'. x = 0.1428571429 Simplifying x = 0.1428571429Solution
x = {-2.666666667, 0.1428571429}
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