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Simplifying gf(0) = 4x2 + 20x Reorder the terms for easier multiplication: 0fg = 4x2 + 20x Anything times zero is zero. 0fg = 4x2 + 20x Reorder the terms: 0 = 20x + 4x2 Solving 0 = 20x + 4x2 Solving for variable 'x'. Remove the zero: -20x + -4x2 = 20x + 4x2 + -20x + -4x2 Reorder the terms: -20x + -4x2 = 20x + -20x + 4x2 + -4x2 Combine like terms: 20x + -20x = 0 -20x + -4x2 = 0 + 4x2 + -4x2 -20x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -20x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-4x'. -4x(5 + x) = 0 Ignore the factor -4.Subproblem 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {0, -5}
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