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Simplifying -1(2x + 7)(2x + 3) = 0 Reorder the terms: -1(7 + 2x)(2x + 3) = 0 Reorder the terms: -1(7 + 2x)(3 + 2x) = 0 Multiply (7 + 2x) * (3 + 2x) -1(7(3 + 2x) + 2x * (3 + 2x)) = 0 -1((3 * 7 + 2x * 7) + 2x * (3 + 2x)) = 0 -1((21 + 14x) + 2x * (3 + 2x)) = 0 -1(21 + 14x + (3 * 2x + 2x * 2x)) = 0 -1(21 + 14x + (6x + 4x2)) = 0 Combine like terms: 14x + 6x = 20x -1(21 + 20x + 4x2) = 0 (21 * -1 + 20x * -1 + 4x2 * -1) = 0 (-21 + -20x + -4x2) = 0 Solving -21 + -20x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 20x + 4x2) = 0 Factor a trinomial. -1((7 + 2x)(3 + 2x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Subproblem 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 = {-3.5, -1.5}
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