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Simplifying 5x(3x + -7) + (3x + -7) = 0 Reorder the terms: 5x(-7 + 3x) + (3x + -7) = 0 (-7 * 5x + 3x * 5x) + (3x + -7) = 0 (-35x + 15x2) + (3x + -7) = 0 Reorder the terms: -35x + 15x2 + (-7 + 3x) = 0 Remove parenthesis around (-7 + 3x) -35x + 15x2 + -7 + 3x = 0 Reorder the terms: -7 + -35x + 3x + 15x2 = 0 Combine like terms: -35x + 3x = -32x -7 + -32x + 15x2 = 0 Solving -7 + -32x + 15x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -5x)(7 + -3x) = 0Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 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 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333Solution
x = {-0.2, 2.333333333}
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