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Simplifying 2106 = (x + 30 + -4)(x + -4)(6) Reorder the terms: 2106 = (30 + -4 + x)(x + -4)(6) Combine like terms: 30 + -4 = 26 2106 = (26 + x)(x + -4)(6) Reorder the terms: 2106 = (26 + x)(-4 + x)(6) Reorder the terms for easier multiplication: 2106 = 6(26 + x)(-4 + x) Multiply (26 + x) * (-4 + x) 2106 = 6(26(-4 + x) + x(-4 + x)) 2106 = 6((-4 * 26 + x * 26) + x(-4 + x)) 2106 = 6((-104 + 26x) + x(-4 + x)) 2106 = 6(-104 + 26x + (-4 * x + x * x)) 2106 = 6(-104 + 26x + (-4x + x2)) Combine like terms: 26x + -4x = 22x 2106 = 6(-104 + 22x + x2) 2106 = (-104 * 6 + 22x * 6 + x2 * 6) 2106 = (-624 + 132x + 6x2) Solving 2106 = -624 + 132x + 6x2 Solving for variable 'x'. Combine like terms: 2106 + 624 = 2730 2730 + -132x + -6x2 = -624 + 132x + 6x2 + 624 + -132x + -6x2 Reorder the terms: 2730 + -132x + -6x2 = -624 + 624 + 132x + -132x + 6x2 + -6x2 Combine like terms: -624 + 624 = 0 2730 + -132x + -6x2 = 0 + 132x + -132x + 6x2 + -6x2 2730 + -132x + -6x2 = 132x + -132x + 6x2 + -6x2 Combine like terms: 132x + -132x = 0 2730 + -132x + -6x2 = 0 + 6x2 + -6x2 2730 + -132x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 2730 + -132x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(455 + -22x + -1x2) = 0 Factor a trinomial. 6((13 + -1x)(35 + x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Subproblem 2
Set the factor '(35 + x)' equal to zero and attempt to solve: Simplifying 35 + x = 0 Solving 35 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + x = 0 + -35 x = 0 + -35 Combine like terms: 0 + -35 = -35 x = -35 Simplifying x = -35Solution
x = {13, -35}
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