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Simplifying (3 + 5x) * 2 + -1(4x + -7)(3 + 5x) = 0 Reorder the terms for easier multiplication: 2(3 + 5x) + -1(4x + -7)(3 + 5x) = 0 (3 * 2 + 5x * 2) + -1(4x + -7)(3 + 5x) = 0 (6 + 10x) + -1(4x + -7)(3 + 5x) = 0 Reorder the terms: 6 + 10x + -1(-7 + 4x)(3 + 5x) = 0 Multiply (-7 + 4x) * (3 + 5x) 6 + 10x + -1(-7(3 + 5x) + 4x * (3 + 5x)) = 0 6 + 10x + -1((3 * -7 + 5x * -7) + 4x * (3 + 5x)) = 0 6 + 10x + -1((-21 + -35x) + 4x * (3 + 5x)) = 0 6 + 10x + -1(-21 + -35x + (3 * 4x + 5x * 4x)) = 0 6 + 10x + -1(-21 + -35x + (12x + 20x2)) = 0 Combine like terms: -35x + 12x = -23x 6 + 10x + -1(-21 + -23x + 20x2) = 0 6 + 10x + (-21 * -1 + -23x * -1 + 20x2 * -1) = 0 6 + 10x + (21 + 23x + -20x2) = 0 Reorder the terms: 6 + 21 + 10x + 23x + -20x2 = 0 Combine like terms: 6 + 21 = 27 27 + 10x + 23x + -20x2 = 0 Combine like terms: 10x + 23x = 33x 27 + 33x + -20x2 = 0 Solving 27 + 33x + -20x2 = 0 Solving for variable 'x'. Factor a trinomial. (9 + -4x)(3 + 5x) = 0Subproblem 1
Set the factor '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25Subproblem 2
Set the factor '(3 + 5x)' equal to zero and attempt to solve: Simplifying 3 + 5x = 0 Solving 3 + 5x = 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 + 5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x = 0 + -3 5x = 0 + -3 Combine like terms: 0 + -3 = -3 5x = -3 Divide each side by '5'. x = -0.6 Simplifying x = -0.6Solution
x = {2.25, -0.6}
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