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Simplifying 6 = (3x + 4)(-1 + -2x) + 6 Reorder the terms: 6 = (4 + 3x)(-1 + -2x) + 6 Multiply (4 + 3x) * (-1 + -2x) 6 = (4(-1 + -2x) + 3x * (-1 + -2x)) + 6 6 = ((-1 * 4 + -2x * 4) + 3x * (-1 + -2x)) + 6 6 = ((-4 + -8x) + 3x * (-1 + -2x)) + 6 6 = (-4 + -8x + (-1 * 3x + -2x * 3x)) + 6 6 = (-4 + -8x + (-3x + -6x2)) + 6 Combine like terms: -8x + -3x = -11x 6 = (-4 + -11x + -6x2) + 6 Reorder the terms: 6 = -4 + 6 + -11x + -6x2 Combine like terms: -4 + 6 = 2 6 = 2 + -11x + -6x2 Solving 6 = 2 + -11x + -6x2 Solving for variable 'x'. Combine like terms: 6 + -2 = 4 4 + 11x + 6x2 = 2 + -11x + -6x2 + -2 + 11x + 6x2 Reorder the terms: 4 + 11x + 6x2 = 2 + -2 + -11x + 11x + -6x2 + 6x2 Combine like terms: 2 + -2 = 0 4 + 11x + 6x2 = 0 + -11x + 11x + -6x2 + 6x2 4 + 11x + 6x2 = -11x + 11x + -6x2 + 6x2 Combine like terms: -11x + 11x = 0 4 + 11x + 6x2 = 0 + -6x2 + 6x2 4 + 11x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 4 + 11x + 6x2 = 0 Factor a trinomial. (4 + 3x)(1 + 2x) = 0Subproblem 1
Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 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 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-1.333333333, -0.5}
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