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Simplifying (2x + 3)(x + -3) = 5 Reorder the terms: (3 + 2x)(x + -3) = 5 Reorder the terms: (3 + 2x)(-3 + x) = 5 Multiply (3 + 2x) * (-3 + x) (3(-3 + x) + 2x * (-3 + x)) = 5 ((-3 * 3 + x * 3) + 2x * (-3 + x)) = 5 ((-9 + 3x) + 2x * (-3 + x)) = 5 (-9 + 3x + (-3 * 2x + x * 2x)) = 5 (-9 + 3x + (-6x + 2x2)) = 5 Combine like terms: 3x + -6x = -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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