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Simplifying (2x + 5w)(7x + -3w) = 0 Reorder the terms: (5w + 2x)(7x + -3w) = 0 Reorder the terms: (5w + 2x)(-3w + 7x) = 0 Multiply (5w + 2x) * (-3w + 7x) (5w * (-3w + 7x) + 2x * (-3w + 7x)) = 0 ((-3w * 5w + 7x * 5w) + 2x * (-3w + 7x)) = 0 Reorder the terms: ((35wx + -15w2) + 2x * (-3w + 7x)) = 0 ((35wx + -15w2) + 2x * (-3w + 7x)) = 0 (35wx + -15w2 + (-3w * 2x + 7x * 2x)) = 0 (35wx + -15w2 + (-6wx + 14x2)) = 0 Reorder the terms: (35wx + -6wx + -15w2 + 14x2) = 0 Combine like terms: 35wx + -6wx = 29wx (29wx + -15w2 + 14x2) = 0 Solving 29wx + -15w2 + 14x2 = 0 Solving for variable 'w'. Factor a trinomial. (-5w + -2x)(3w + -7x) = 0Subproblem 1
Set the factor '(-5w + -2x)' equal to zero and attempt to solve: Simplifying -5w + -2x = 0 Solving -5w + -2x = 0 Move all terms containing w to the left, all other terms to the right. Add '2x' to each side of the equation. -5w + -2x + 2x = 0 + 2x Combine like terms: -2x + 2x = 0 -5w + 0 = 0 + 2x -5w = 0 + 2x Remove the zero: -5w = 2x Divide each side by '-5'. w = -0.4x Simplifying w = -0.4xSubproblem 2
Set the factor '(3w + -7x)' equal to zero and attempt to solve: Simplifying 3w + -7x = 0 Solving 3w + -7x = 0 Move all terms containing w to the left, all other terms to the right. Add '7x' to each side of the equation. 3w + -7x + 7x = 0 + 7x Combine like terms: -7x + 7x = 0 3w + 0 = 0 + 7x 3w = 0 + 7x Remove the zero: 3w = 7x Divide each side by '3'. w = 2.333333333x Simplifying w = 2.333333333xSolution
w = {-0.4x, 2.333333333x}
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