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Simplifying (2x + -3)(3x + 5) = 6x(x + 7) Reorder the terms: (-3 + 2x)(3x + 5) = 6x(x + 7) Reorder the terms: (-3 + 2x)(5 + 3x) = 6x(x + 7) Multiply (-3 + 2x) * (5 + 3x) (-3(5 + 3x) + 2x * (5 + 3x)) = 6x(x + 7) ((5 * -3 + 3x * -3) + 2x * (5 + 3x)) = 6x(x + 7) ((-15 + -9x) + 2x * (5 + 3x)) = 6x(x + 7) (-15 + -9x + (5 * 2x + 3x * 2x)) = 6x(x + 7) (-15 + -9x + (10x + 6x2)) = 6x(x + 7) Combine like terms: -9x + 10x = 1x (-15 + 1x + 6x2) = 6x(x + 7) Reorder the terms: -15 + 1x + 6x2 = 6x(7 + x) -15 + 1x + 6x2 = (7 * 6x + x * 6x) -15 + 1x + 6x2 = (42x + 6x2) Add '-6x2' to each side of the equation. -15 + 1x + 6x2 + -6x2 = 42x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -15 + 1x + 0 = 42x + 6x2 + -6x2 -15 + 1x = 42x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -15 + 1x = 42x + 0 -15 + 1x = 42x Solving -15 + 1x = 42x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42x' to each side of the equation. -15 + 1x + -42x = 42x + -42x Combine like terms: 1x + -42x = -41x -15 + -41x = 42x + -42x Combine like terms: 42x + -42x = 0 -15 + -41x = 0 Add '15' to each side of the equation. -15 + 15 + -41x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -41x = 0 + 15 -41x = 0 + 15 Combine like terms: 0 + 15 = 15 -41x = 15 Divide each side by '-41'. x = -0.3658536585 Simplifying x = -0.3658536585
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