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Simplifying (3x + 2)(5x + 1) = ax * 2 + bx + 2 Reorder the terms: (2 + 3x)(5x + 1) = ax * 2 + bx + 2 Reorder the terms: (2 + 3x)(1 + 5x) = ax * 2 + bx + 2 Multiply (2 + 3x) * (1 + 5x) (2(1 + 5x) + 3x * (1 + 5x)) = ax * 2 + bx + 2 ((1 * 2 + 5x * 2) + 3x * (1 + 5x)) = ax * 2 + bx + 2 ((2 + 10x) + 3x * (1 + 5x)) = ax * 2 + bx + 2 (2 + 10x + (1 * 3x + 5x * 3x)) = ax * 2 + bx + 2 (2 + 10x + (3x + 15x2)) = ax * 2 + bx + 2 Combine like terms: 10x + 3x = 13x (2 + 13x + 15x2) = ax * 2 + bx + 2 Reorder the terms for easier multiplication: 2 + 13x + 15x2 = 2ax + bx + 2 Reorder the terms: 2 + 13x + 15x2 = 2 + 2ax + bx Add '-2' to each side of the equation. 2 + 13x + -2 + 15x2 = 2 + 2ax + -2 + bx Reorder the terms: 2 + -2 + 13x + 15x2 = 2 + 2ax + -2 + bx Combine like terms: 2 + -2 = 0 0 + 13x + 15x2 = 2 + 2ax + -2 + bx 13x + 15x2 = 2 + 2ax + -2 + bx Reorder the terms: 13x + 15x2 = 2 + -2 + 2ax + bx Combine like terms: 2 + -2 = 0 13x + 15x2 = 0 + 2ax + bx 13x + 15x2 = 2ax + bx Solving 13x + 15x2 = 2ax + bx Solving for variable 'x'. Reorder the terms: -2ax + -1bx + 13x + 15x2 = 2ax + bx + -2ax + -1bx Reorder the terms: -2ax + -1bx + 13x + 15x2 = 2ax + -2ax + bx + -1bx Combine like terms: 2ax + -2ax = 0 -2ax + -1bx + 13x + 15x2 = 0 + bx + -1bx -2ax + -1bx + 13x + 15x2 = bx + -1bx Combine like terms: bx + -1bx = 0 -2ax + -1bx + 13x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-2a + -1b + 13 + 15x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-2a + -1b + 13 + 15x)' equal to zero and attempt to solve: Simplifying -2a + -1b + 13 + 15x = 0 Reorder the terms: 13 + -2a + -1b + 15x = 0 Solving 13 + -2a + -1b + 15x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -2a + -1b + -13 + 15x = 0 + -13 Reorder the terms: 13 + -13 + -2a + -1b + 15x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2a + -1b + 15x = 0 + -13 -2a + -1b + 15x = 0 + -13 Combine like terms: 0 + -13 = -13 -2a + -1b + 15x = -13 Add '2a' to each side of the equation. -2a + -1b + 2a + 15x = -13 + 2a Reorder the terms: -2a + 2a + -1b + 15x = -13 + 2a Combine like terms: -2a + 2a = 0 0 + -1b + 15x = -13 + 2a -1b + 15x = -13 + 2a Add 'b' to each side of the equation. -1b + b + 15x = -13 + 2a + b Combine like terms: -1b + b = 0 0 + 15x = -13 + 2a + b 15x = -13 + 2a + b Divide each side by '15'. x = -0.8666666667 + 0.1333333333a + 0.06666666667b Simplifying x = -0.8666666667 + 0.1333333333a + 0.06666666667bSolution
x = {0, -0.8666666667 + 0.1333333333a + 0.06666666667b}
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