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Simplifying (4x + 5)(2x + 3) = 3 Reorder the terms: (5 + 4x)(2x + 3) = 3 Reorder the terms: (5 + 4x)(3 + 2x) = 3 Multiply (5 + 4x) * (3 + 2x) (5(3 + 2x) + 4x * (3 + 2x)) = 3 ((3 * 5 + 2x * 5) + 4x * (3 + 2x)) = 3 ((15 + 10x) + 4x * (3 + 2x)) = 3 (15 + 10x + (3 * 4x + 2x * 4x)) = 3 (15 + 10x + (12x + 8x2)) = 3 Combine like terms: 10x + 12x = 22x (15 + 22x + 8x2) = 3 Solving 15 + 22x + 8x2 = 3 Solving for variable 'x'. Reorder the terms: 15 + -3 + 22x + 8x2 = 3 + -3 Combine like terms: 15 + -3 = 12 12 + 22x + 8x2 = 3 + -3 Combine like terms: 3 + -3 = 0 12 + 22x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 11x + 4x2) = 0 Factor a trinomial. 2((2 + x)(3 + 4x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Solution
x = {-2, -0.75}
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