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Simplifying (5x + -1)(4 + -4x) = 0 Reorder the terms: (-1 + 5x)(4 + -4x) = 0 Multiply (-1 + 5x) * (4 + -4x) (-1(4 + -4x) + 5x * (4 + -4x)) = 0 ((4 * -1 + -4x * -1) + 5x * (4 + -4x)) = 0 ((-4 + 4x) + 5x * (4 + -4x)) = 0 (-4 + 4x + (4 * 5x + -4x * 5x)) = 0 (-4 + 4x + (20x + -20x2)) = 0 Combine like terms: 4x + 20x = 24x (-4 + 24x + -20x2) = 0 Solving -4 + 24x + -20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + 6x + -5x2) = 0 Factor a trinomial. 4((-1 + x)(1 + -5x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Solution
x = {1, 0.2}
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