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Simplifying (2x2 + x)(2x + 1) = 0 Reorder the terms: (x + 2x2)(2x + 1) = 0 Reorder the terms: (x + 2x2)(1 + 2x) = 0 Multiply (x + 2x2) * (1 + 2x) (x(1 + 2x) + 2x2 * (1 + 2x)) = 0 ((1 * x + 2x * x) + 2x2 * (1 + 2x)) = 0 ((1x + 2x2) + 2x2 * (1 + 2x)) = 0 (1x + 2x2 + (1 * 2x2 + 2x * 2x2)) = 0 (1x + 2x2 + (2x2 + 4x3)) = 0 Combine like terms: 2x2 + 2x2 = 4x2 (1x + 4x2 + 4x3) = 0 Solving 1x + 4x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 4x + 4x2) = 0 Factor a trinomial. x((1 + 2x)(1 + 2x)) = 0Subproblem 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 '(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 = -0.5Subproblem 3
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 = {0, -0.5, -0.5}
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