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Simplifying f(0) = 9x(x + -14)(x + 10) Reorder the terms for easier multiplication: 0f = 9x(x + -14)(x + 10) Anything times zero is zero. 0f = 9x(x + -14)(x + 10) Reorder the terms: 0 = 9x(-14 + x)(x + 10) Reorder the terms: 0 = 9x(-14 + x)(10 + x) Multiply (-14 + x) * (10 + x) 0 = 9x(-14(10 + x) + x(10 + x)) 0 = 9x((10 * -14 + x * -14) + x(10 + x)) 0 = 9x((-140 + -14x) + x(10 + x)) 0 = 9x(-140 + -14x + (10 * x + x * x)) 0 = 9x(-140 + -14x + (10x + x2)) Combine like terms: -14x + 10x = -4x 0 = 9x(-140 + -4x + x2) 0 = (-140 * 9x + -4x * 9x + x2 * 9x) 0 = (-1260x + -36x2 + 9x3) Solving 0 = -1260x + -36x2 + 9x3 Solving for variable 'x'. Remove the zero: 1260x + 36x2 + -9x3 = -1260x + -36x2 + 9x3 + 1260x + 36x2 + -9x3 Reorder the terms: 1260x + 36x2 + -9x3 = -1260x + 1260x + -36x2 + 36x2 + 9x3 + -9x3 Combine like terms: -1260x + 1260x = 0 1260x + 36x2 + -9x3 = 0 + -36x2 + 36x2 + 9x3 + -9x3 1260x + 36x2 + -9x3 = -36x2 + 36x2 + 9x3 + -9x3 Combine like terms: -36x2 + 36x2 = 0 1260x + 36x2 + -9x3 = 0 + 9x3 + -9x3 1260x + 36x2 + -9x3 = 9x3 + -9x3 Combine like terms: 9x3 + -9x3 = 0 1260x + 36x2 + -9x3 = 0 Factor out the Greatest Common Factor (GCF), '9x'. 9x(140 + 4x + -1x2) = 0 Factor a trinomial. 9x((14 + -1x)(10 + x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14Subproblem 3
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Solution
x = {0, 14, -10}
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