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Simplifying (4x + -1)(3x + -1) = 0 Reorder the terms: (-1 + 4x)(3x + -1) = 0 Reorder the terms: (-1 + 4x)(-1 + 3x) = 0 Multiply (-1 + 4x) * (-1 + 3x) (-1(-1 + 3x) + 4x * (-1 + 3x)) = 0 ((-1 * -1 + 3x * -1) + 4x * (-1 + 3x)) = 0 ((1 + -3x) + 4x * (-1 + 3x)) = 0 (1 + -3x + (-1 * 4x + 3x * 4x)) = 0 (1 + -3x + (-4x + 12x^{2})) = 0 Combine like terms: -3x + -4x = -7x (1 + -7x + 12x^{2}) = 0 Solving 1 + -7x + 12x^{2}= 0 Solving for variable 'x'. Factor a trinomial. (1 + -4x)(1 + -3x) = 0## Subproblem 1

Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25## Subproblem 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 = 0.3333333333## Solution

x = {0.25, 0.3333333333}

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