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Simplifying (2x + 3)(2x + 3) = 6 + 4x Reorder the terms: (3 + 2x)(2x + 3) = 6 + 4x Reorder the terms: (3 + 2x)(3 + 2x) = 6 + 4x Multiply (3 + 2x) * (3 + 2x) (3(3 + 2x) + 2x * (3 + 2x)) = 6 + 4x ((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 6 + 4x ((9 + 6x) + 2x * (3 + 2x)) = 6 + 4x (9 + 6x + (3 * 2x + 2x * 2x)) = 6 + 4x (9 + 6x + (6x + 4x2)) = 6 + 4x Combine like terms: 6x + 6x = 12x (9 + 12x + 4x2) = 6 + 4x Solving 9 + 12x + 4x2 = 6 + 4x Solving for variable 'x'. Reorder the terms: 9 + -6 + 12x + -4x + 4x2 = 6 + 4x + -6 + -4x Combine like terms: 9 + -6 = 3 3 + 12x + -4x + 4x2 = 6 + 4x + -6 + -4x Combine like terms: 12x + -4x = 8x 3 + 8x + 4x2 = 6 + 4x + -6 + -4x Reorder the terms: 3 + 8x + 4x2 = 6 + -6 + 4x + -4x Combine like terms: 6 + -6 = 0 3 + 8x + 4x2 = 0 + 4x + -4x 3 + 8x + 4x2 = 4x + -4x Combine like terms: 4x + -4x = 0 3 + 8x + 4x2 = 0 Factor a trinomial. (3 + 2x)(1 + 2x) = 0Subproblem 1
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 = -1.5Subproblem 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 = {-1.5, -0.5}
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