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Simplifying 4(2x + 1)(x + 2) = 0 Reorder the terms: 4(1 + 2x)(x + 2) = 0 Reorder the terms: 4(1 + 2x)(2 + x) = 0 Multiply (1 + 2x) * (2 + x) 4(1(2 + x) + 2x * (2 + x)) = 0 4((2 * 1 + x * 1) + 2x * (2 + x)) = 0 4((2 + 1x) + 2x * (2 + x)) = 0 4(2 + 1x + (2 * 2x + x * 2x)) = 0 4(2 + 1x + (4x + 2x2)) = 0 Combine like terms: 1x + 4x = 5x 4(2 + 5x + 2x2) = 0 (2 * 4 + 5x * 4 + 2x2 * 4) = 0 (8 + 20x + 8x2) = 0 Solving 8 + 20x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + 5x + 2x2) = 0 Factor a trinomial. 4((2 + x)(1 + 2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 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 = {-2, -0.5}
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