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Simplifying (2x2 + 3x)(x + 2) = 0 Reorder the terms: (3x + 2x2)(x + 2) = 0 Reorder the terms: (3x + 2x2)(2 + x) = 0 Multiply (3x + 2x2) * (2 + x) (3x * (2 + x) + 2x2 * (2 + x)) = 0 ((2 * 3x + x * 3x) + 2x2 * (2 + x)) = 0 ((6x + 3x2) + 2x2 * (2 + x)) = 0 (6x + 3x2 + (2 * 2x2 + x * 2x2)) = 0 (6x + 3x2 + (4x2 + 2x3)) = 0 Combine like terms: 3x2 + 4x2 = 7x2 (6x + 7x2 + 2x3) = 0 Solving 6x + 7x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(6 + 7x + 2x2) = 0 Factor a trinomial. x((2 + x)(3 + 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 '(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 3
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {0, -2, -1.5}
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