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Simplifying 2x(x + 2) + 3(x + 2) = 0 Reorder the terms: 2x(2 + x) + 3(x + 2) = 0 (2 * 2x + x * 2x) + 3(x + 2) = 0 (4x + 2x2) + 3(x + 2) = 0 Reorder the terms: 4x + 2x2 + 3(2 + x) = 0 4x + 2x2 + (2 * 3 + x * 3) = 0 4x + 2x2 + (6 + 3x) = 0 Reorder the terms: 6 + 4x + 3x + 2x2 = 0 Combine like terms: 4x + 3x = 7x 6 + 7x + 2x2 = 0 Solving 6 + 7x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (2 + x)(3 + 2x) = 0Subproblem 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 '(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 = {-2, -1.5}
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