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Simplifying (2x + -1)(x2 + -4x + x) = 0 Reorder the terms: (-1 + 2x)(x2 + -4x + x) = 0 Reorder the terms: (-1 + 2x)(-4x + x + x2) = 0 Combine like terms: -4x + x = -3x (-1 + 2x)(-3x + x2) = 0 Multiply (-1 + 2x) * (-3x + x2) (-1(-3x + x2) + 2x * (-3x + x2)) = 0 ((-3x * -1 + x2 * -1) + 2x * (-3x + x2)) = 0 ((3x + -1x2) + 2x * (-3x + x2)) = 0 (3x + -1x2 + (-3x * 2x + x2 * 2x)) = 0 (3x + -1x2 + (-6x2 + 2x3)) = 0 Combine like terms: -1x2 + -6x2 = -7x2 (3x + -7x2 + 2x3) = 0 Solving 3x + -7x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + -7x + 2x2) = 0 Factor a trinomial. x((1 + -2x)(3 + -1x)) = 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 + -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 = 0.5Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, 0.5, 3}
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