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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 = 1x -6 + 1x + 2x2 = 0 Solving -6 + 1x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (-2 + -1x)(3 + -2x) = 0Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. 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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