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Simplifying (7x + 3)(5x + -2) = 6 Reorder the terms: (3 + 7x)(5x + -2) = 6 Reorder the terms: (3 + 7x)(-2 + 5x) = 6 Multiply (3 + 7x) * (-2 + 5x) (3(-2 + 5x) + 7x * (-2 + 5x)) = 6 ((-2 * 3 + 5x * 3) + 7x * (-2 + 5x)) = 6 ((-6 + 15x) + 7x * (-2 + 5x)) = 6 (-6 + 15x + (-2 * 7x + 5x * 7x)) = 6 (-6 + 15x + (-14x + 35x2)) = 6 Combine like terms: 15x + -14x = 1x (-6 + 1x + 35x2) = 6 Solving -6 + 1x + 35x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + -6 + 1x + 35x2 = 6 + -6 Combine like terms: -6 + -6 = -12 -12 + 1x + 35x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -12 + 1x + 35x2 = 0 Factor a trinomial. (-3 + -5x)(4 + -7x) = 0Subproblem 1
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 = -0.6Subproblem 2
Set the factor '(4 + -7x)' equal to zero and attempt to solve: Simplifying 4 + -7x = 0 Solving 4 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7x = 0 + -4 -7x = 0 + -4 Combine like terms: 0 + -4 = -4 -7x = -4 Divide each side by '-7'. x = 0.5714285714 Simplifying x = 0.5714285714Solution
x = {-0.6, 0.5714285714}
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