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Simplifying (9x3 + 5x2 + -4x) + -1(5x3 + -2x2 + -6x) + -1(4x3 + 6x2 + 24) = 0 Reorder the terms: (-4x + 5x2 + 9x3) + -1(5x3 + -2x2 + -6x) + -1(4x3 + 6x2 + 24) = 0 Remove parenthesis around (-4x + 5x2 + 9x3) -4x + 5x2 + 9x3 + -1(5x3 + -2x2 + -6x) + -1(4x3 + 6x2 + 24) = 0 Reorder the terms: -4x + 5x2 + 9x3 + -1(-6x + -2x2 + 5x3) + -1(4x3 + 6x2 + 24) = 0 -4x + 5x2 + 9x3 + (-6x * -1 + -2x2 * -1 + 5x3 * -1) + -1(4x3 + 6x2 + 24) = 0 -4x + 5x2 + 9x3 + (6x + 2x2 + -5x3) + -1(4x3 + 6x2 + 24) = 0 Reorder the terms: -4x + 5x2 + 9x3 + 6x + 2x2 + -5x3 + -1(24 + 6x2 + 4x3) = 0 -4x + 5x2 + 9x3 + 6x + 2x2 + -5x3 + (24 * -1 + 6x2 * -1 + 4x3 * -1) = 0 -4x + 5x2 + 9x3 + 6x + 2x2 + -5x3 + (-24 + -6x2 + -4x3) = 0 Reorder the terms: -24 + -4x + 6x + 5x2 + 2x2 + -6x2 + 9x3 + -5x3 + -4x3 = 0 Combine like terms: -4x + 6x = 2x -24 + 2x + 5x2 + 2x2 + -6x2 + 9x3 + -5x3 + -4x3 = 0 Combine like terms: 5x2 + 2x2 = 7x2 -24 + 2x + 7x2 + -6x2 + 9x3 + -5x3 + -4x3 = 0 Combine like terms: 7x2 + -6x2 = 1x2 -24 + 2x + 1x2 + 9x3 + -5x3 + -4x3 = 0 Combine like terms: 9x3 + -5x3 = 4x3 -24 + 2x + 1x2 + 4x3 + -4x3 = 0 Combine like terms: 4x3 + -4x3 = 0 -24 + 2x + 1x2 + 0 = 0 -24 + 2x + 1x2 = 0 Solving -24 + 2x + 1x2 = 0 Solving for variable 'x'. Factor a trinomial. (-6 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 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 = {-6, 4}
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