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Simplifying -1[9x(2x + 6)] = -3 + -1[4(3x + -4) + -3x] Reorder the terms: -1[9x(6 + 2x)] = -3 + -1[4(3x + -4) + -3x] -1[(6 * 9x + 2x * 9x)] = -3 + -1[4(3x + -4) + -3x] -1[(54x + 18x2)] = -3 + -1[4(3x + -4) + -3x] [54x * -1 + 18x2 * -1] = -3 + -1[4(3x + -4) + -3x] [-54x + -18x2] = -3 + -1[4(3x + -4) + -3x] Reorder the terms: -54x + -18x2 = -3 + -1[4(-4 + 3x) + -3x] -54x + -18x2 = -3 + -1[(-4 * 4 + 3x * 4) + -3x] -54x + -18x2 = -3 + -1[(-16 + 12x) + -3x] Combine like terms: 12x + -3x = 9x -54x + -18x2 = -3 + -1[-16 + 9x] -54x + -18x2 = -3 + [-16 * -1 + 9x * -1] -54x + -18x2 = -3 + [16 + -9x] Combine like terms: -3 + 16 = 13 -54x + -18x2 = 13 + -9x Solving -54x + -18x2 = 13 + -9x Solving for variable 'x'. Reorder the terms: -13 + -54x + 9x + -18x2 = 13 + -9x + -13 + 9x Combine like terms: -54x + 9x = -45x -13 + -45x + -18x2 = 13 + -9x + -13 + 9x Reorder the terms: -13 + -45x + -18x2 = 13 + -13 + -9x + 9x Combine like terms: 13 + -13 = 0 -13 + -45x + -18x2 = 0 + -9x + 9x -13 + -45x + -18x2 = -9x + 9x Combine like terms: -9x + 9x = 0 -13 + -45x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 45x + 18x2) = 0 Factor a trinomial. -1((13 + 6x)(1 + 3x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 6x)' equal to zero and attempt to solve: Simplifying 13 + 6x = 0 Solving 13 + 6x = 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 + 6x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 6x = 0 + -13 6x = 0 + -13 Combine like terms: 0 + -13 = -13 6x = -13 Divide each side by '6'. x = -2.166666667 Simplifying x = -2.166666667Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-2.166666667, -0.3333333333}
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