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Simplifying (x + 1)(3x + -4) * x = 0 Reorder the terms: (1 + x)(3x + -4) * x = 0 Reorder the terms: (1 + x)(-4 + 3x) * x = 0 Reorder the terms for easier multiplication: x(1 + x)(-4 + 3x) = 0 Multiply (1 + x) * (-4 + 3x) x(1(-4 + 3x) + x(-4 + 3x)) = 0 x((-4 * 1 + 3x * 1) + x(-4 + 3x)) = 0 x((-4 + 3x) + x(-4 + 3x)) = 0 x(-4 + 3x + (-4 * x + 3x * x)) = 0 x(-4 + 3x + (-4x + 3x2)) = 0 Combine like terms: 3x + -4x = -1x x(-4 + -1x + 3x2) = 0 (-4 * x + -1x * x + 3x2 * x) = 0 (-4x + -1x2 + 3x3) = 0 Solving -4x + -1x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + -1x + 3x2) = 0 Factor a trinomial. x((-1 + -1x)(4 + -3x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
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 3
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 = 1.333333333Solution
x = {0, -1, 1.333333333}
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