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Simplifying 6x(3x + 1) + 1(3x + 1) = 0 Reorder the terms: 6x(1 + 3x) + 1(3x + 1) = 0 (1 * 6x + 3x * 6x) + 1(3x + 1) = 0 (6x + 18x2) + 1(3x + 1) = 0 Reorder the terms: 6x + 18x2 + 1(1 + 3x) = 0 6x + 18x2 + (1 * 1 + 3x * 1) = 0 6x + 18x2 + (1 + 3x) = 0 Reorder the terms: 1 + 6x + 3x + 18x2 = 0 Combine like terms: 6x + 3x = 9x 1 + 9x + 18x2 = 0 Solving 1 + 9x + 18x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + 3x)(1 + 6x) = 0Subproblem 1
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 = -0.3333333333Subproblem 2
Set the factor '(1 + 6x)' equal to zero and attempt to solve: Simplifying 1 + 6x = 0 Solving 1 + 6x = 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 + 6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x = 0 + -1 6x = 0 + -1 Combine like terms: 0 + -1 = -1 6x = -1 Divide each side by '6'. x = -0.1666666667 Simplifying x = -0.1666666667Solution
x = {-0.3333333333, -0.1666666667}
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