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Simplifying 5x(3x + -1) + 7(3x + -1) = 0 Reorder the terms: 5x(-1 + 3x) + 7(3x + -1) = 0 (-1 * 5x + 3x * 5x) + 7(3x + -1) = 0 (-5x + 15x2) + 7(3x + -1) = 0 Reorder the terms: -5x + 15x2 + 7(-1 + 3x) = 0 -5x + 15x2 + (-1 * 7 + 3x * 7) = 0 -5x + 15x2 + (-7 + 21x) = 0 Reorder the terms: -7 + -5x + 21x + 15x2 = 0 Combine like terms: -5x + 21x = 16x -7 + 16x + 15x2 = 0 Solving -7 + 16x + 15x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -5x)(1 + -3x) = 0Subproblem 1
Set the factor '(-7 + -5x)' equal to zero and attempt to solve: Simplifying -7 + -5x = 0 Solving -7 + -5x = 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 + -5x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5x = 0 + 7 -5x = 0 + 7 Combine like terms: 0 + 7 = 7 -5x = 7 Divide each side by '-5'. x = -1.4 Simplifying x = -1.4Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-1.4, 0.3333333333}
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