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Simplifying (x + 5)(4x + -2) = 0 Reorder the terms: (5 + x)(4x + -2) = 0 Reorder the terms: (5 + x)(-2 + 4x) = 0 Multiply (5 + x) * (-2 + 4x) (5(-2 + 4x) + x(-2 + 4x)) = 0 ((-2 * 5 + 4x * 5) + x(-2 + 4x)) = 0 ((-10 + 20x) + x(-2 + 4x)) = 0 (-10 + 20x + (-2 * x + 4x * x)) = 0 (-10 + 20x + (-2x + 4x2)) = 0 Combine like terms: 20x + -2x = 18x (-10 + 18x + 4x2) = 0 Solving -10 + 18x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 9x + 2x2) = 0 Factor a trinomial. 2((-5 + -1x)(1 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 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 = 0.5Solution
x = {-5, 0.5}
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