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Simplifying (4x + 2)(2x + 7) = 0 Reorder the terms: (2 + 4x)(2x + 7) = 0 Reorder the terms: (2 + 4x)(7 + 2x) = 0 Multiply (2 + 4x) * (7 + 2x) (2(7 + 2x) + 4x * (7 + 2x)) = 0 ((7 * 2 + 2x * 2) + 4x * (7 + 2x)) = 0 ((14 + 4x) + 4x * (7 + 2x)) = 0 (14 + 4x + (7 * 4x + 2x * 4x)) = 0 (14 + 4x + (28x + 8x2)) = 0 Combine like terms: 4x + 28x = 32x (14 + 32x + 8x2) = 0 Solving 14 + 32x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 16x + 4x2) = 0 Factor a trinomial. 2((7 + 2x)(1 + 2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 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 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Subproblem 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 = {-3.5, -0.5}
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