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