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Simplifying (3x + 2)(4x + 1) + -3 = 0 Reorder the terms: (2 + 3x)(4x + 1) + -3 = 0 Reorder the terms: (2 + 3x)(1 + 4x) + -3 = 0 Multiply (2 + 3x) * (1 + 4x) (2(1 + 4x) + 3x * (1 + 4x)) + -3 = 0 ((1 * 2 + 4x * 2) + 3x * (1 + 4x)) + -3 = 0 ((2 + 8x) + 3x * (1 + 4x)) + -3 = 0 (2 + 8x + (1 * 3x + 4x * 3x)) + -3 = 0 (2 + 8x + (3x + 12x2)) + -3 = 0 Combine like terms: 8x + 3x = 11x (2 + 11x + 12x2) + -3 = 0 Reorder the terms: 2 + -3 + 11x + 12x2 = 0 Combine like terms: 2 + -3 = -1 -1 + 11x + 12x2 = 0 Solving -1 + 11x + 12x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x)(1 + -12x) = 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 + -12x)' equal to zero and attempt to solve: Simplifying 1 + -12x = 0 Solving 1 + -12x = 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 + -12x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -12x = 0 + -1 -12x = 0 + -1 Combine like terms: 0 + -1 = -1 -12x = -1 Divide each side by '-12'. x = 0.08333333333 Simplifying x = 0.08333333333Solution
x = {-1, 0.08333333333}
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