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Simplifying (x + -3)(2x + 3) = 5 Reorder the terms: (-3 + x)(2x + 3) = 5 Reorder the terms: (-3 + x)(3 + 2x) = 5 Multiply (-3 + x) * (3 + 2x) (-3(3 + 2x) + x(3 + 2x)) = 5 ((3 * -3 + 2x * -3) + x(3 + 2x)) = 5 ((-9 + -6x) + x(3 + 2x)) = 5 (-9 + -6x + (3 * x + 2x * x)) = 5 (-9 + -6x + (3x + 2x2)) = 5 Combine like terms: -6x + 3x = -3x (-9 + -3x + 2x2) = 5 Solving -9 + -3x + 2x2 = 5 Solving for variable 'x'. Reorder the terms: -9 + -5 + -3x + 2x2 = 5 + -5 Combine like terms: -9 + -5 = -14 -14 + -3x + 2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -14 + -3x + 2x2 = 0 Factor a trinomial. (-2 + -1x)(7 + -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 '(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 = 3.5Solution
x = {-2, 3.5}
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