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Simplifying (3x + -8)(4x + 1) = 0 Reorder the terms: (-8 + 3x)(4x + 1) = 0 Reorder the terms: (-8 + 3x)(1 + 4x) = 0 Multiply (-8 + 3x) * (1 + 4x) (-8(1 + 4x) + 3x * (1 + 4x)) = 0 ((1 * -8 + 4x * -8) + 3x * (1 + 4x)) = 0 ((-8 + -32x) + 3x * (1 + 4x)) = 0 (-8 + -32x + (1 * 3x + 4x * 3x)) = 0 (-8 + -32x + (3x + 12x2)) = 0 Combine like terms: -32x + 3x = -29x (-8 + -29x + 12x2) = 0 Solving -8 + -29x + 12x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -4x)(8 + -3x) = 0Subproblem 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 = -0.25Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve: Simplifying 8 + -3x = 0 Solving 8 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x = 0 + -8 -3x = 0 + -8 Combine like terms: 0 + -8 = -8 -3x = -8 Divide each side by '-3'. x = 2.666666667 Simplifying x = 2.666666667Solution
x = {-0.25, 2.666666667}
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