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Simplifying (4x + 1)(x + 4) = 0 Reorder the terms: (1 + 4x)(x + 4) = 0 Reorder the terms: (1 + 4x)(4 + x) = 0 Multiply (1 + 4x) * (4 + x) (1(4 + x) + 4x * (4 + x)) = 0 ((4 * 1 + x * 1) + 4x * (4 + x)) = 0 ((4 + 1x) + 4x * (4 + x)) = 0 (4 + 1x + (4 * 4x + x * 4x)) = 0 (4 + 1x + (16x + 4x2)) = 0 Combine like terms: 1x + 16x = 17x (4 + 17x + 4x2) = 0 Solving 4 + 17x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (4 + x)(1 + 4x) = 0Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {-4, -0.25}
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