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Simplifying (3x + 1)(2x + 5) = 4(2x + 5) Reorder the terms: (1 + 3x)(2x + 5) = 4(2x + 5) Reorder the terms: (1 + 3x)(5 + 2x) = 4(2x + 5) Multiply (1 + 3x) * (5 + 2x) (1(5 + 2x) + 3x * (5 + 2x)) = 4(2x + 5) ((5 * 1 + 2x * 1) + 3x * (5 + 2x)) = 4(2x + 5) ((5 + 2x) + 3x * (5 + 2x)) = 4(2x + 5) (5 + 2x + (5 * 3x + 2x * 3x)) = 4(2x + 5) (5 + 2x + (15x + 6x2)) = 4(2x + 5) Combine like terms: 2x + 15x = 17x (5 + 17x + 6x2) = 4(2x + 5) Reorder the terms: 5 + 17x + 6x2 = 4(5 + 2x) 5 + 17x + 6x2 = (5 * 4 + 2x * 4) 5 + 17x + 6x2 = (20 + 8x) Solving 5 + 17x + 6x2 = 20 + 8x Solving for variable 'x'. Reorder the terms: 5 + -20 + 17x + -8x + 6x2 = 20 + 8x + -20 + -8x Combine like terms: 5 + -20 = -15 -15 + 17x + -8x + 6x2 = 20 + 8x + -20 + -8x Combine like terms: 17x + -8x = 9x -15 + 9x + 6x2 = 20 + 8x + -20 + -8x Reorder the terms: -15 + 9x + 6x2 = 20 + -20 + 8x + -8x Combine like terms: 20 + -20 = 0 -15 + 9x + 6x2 = 0 + 8x + -8x -15 + 9x + 6x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -15 + 9x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 3x + 2x2) = 0 Factor a trinomial. 3((-5 + -2x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-2.5, 1}
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