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Simplifying (x + 7)(4x + 1) = 0 Reorder the terms: (7 + x)(4x + 1) = 0 Reorder the terms: (7 + x)(1 + 4x) = 0 Multiply (7 + x) * (1 + 4x) (7(1 + 4x) + x(1 + 4x)) = 0 ((1 * 7 + 4x * 7) + x(1 + 4x)) = 0 ((7 + 28x) + x(1 + 4x)) = 0 (7 + 28x + (1 * x + 4x * x)) = 0 (7 + 28x + (1x + 4x2)) = 0 Combine like terms: 28x + 1x = 29x (7 + 29x + 4x2) = 0 Solving 7 + 29x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (7 + x)(1 + 4x) = 0Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 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 = {-7, -0.25}
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