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Simplifying 1 + -1(3x + 1)(3x + 1) = 0 Reorder the terms: 1 + -1(1 + 3x)(3x + 1) = 0 Reorder the terms: 1 + -1(1 + 3x)(1 + 3x) = 0 Multiply (1 + 3x) * (1 + 3x) 1 + -1(1(1 + 3x) + 3x * (1 + 3x)) = 0 1 + -1((1 * 1 + 3x * 1) + 3x * (1 + 3x)) = 0 1 + -1((1 + 3x) + 3x * (1 + 3x)) = 0 1 + -1(1 + 3x + (1 * 3x + 3x * 3x)) = 0 1 + -1(1 + 3x + (3x + 9x2)) = 0 Combine like terms: 3x + 3x = 6x 1 + -1(1 + 6x + 9x2) = 0 1 + (1 * -1 + 6x * -1 + 9x2 * -1) = 0 1 + (-1 + -6x + -9x2) = 0 Combine like terms: 1 + -1 = 0 0 + -6x + -9x2 = 0 -6x + -9x2 = 0 Solving -6x + -9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-3x'. -3x(2 + 3x) = 0 Ignore the factor -3.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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {0, -0.6666666667}
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