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Simplifying (3x + 5w)(3x + -8w) = 0 Reorder the terms: (5w + 3x)(3x + -8w) = 0 Reorder the terms: (5w + 3x)(-8w + 3x) = 0 Multiply (5w + 3x) * (-8w + 3x) (5w * (-8w + 3x) + 3x * (-8w + 3x)) = 0 ((-8w * 5w + 3x * 5w) + 3x * (-8w + 3x)) = 0 Reorder the terms: ((15wx + -40w2) + 3x * (-8w + 3x)) = 0 ((15wx + -40w2) + 3x * (-8w + 3x)) = 0 (15wx + -40w2 + (-8w * 3x + 3x * 3x)) = 0 (15wx + -40w2 + (-24wx + 9x2)) = 0 Reorder the terms: (15wx + -24wx + -40w2 + 9x2) = 0 Combine like terms: 15wx + -24wx = -9wx (-9wx + -40w2 + 9x2) = 0 Solving -9wx + -40w2 + 9x2 = 0 Solving for variable 'w'. Factor a trinomial. (-5w + -3x)(8w + -3x) = 0Subproblem 1
Set the factor '(-5w + -3x)' equal to zero and attempt to solve: Simplifying -5w + -3x = 0 Solving -5w + -3x = 0 Move all terms containing w to the left, all other terms to the right. Add '3x' to each side of the equation. -5w + -3x + 3x = 0 + 3x Combine like terms: -3x + 3x = 0 -5w + 0 = 0 + 3x -5w = 0 + 3x Remove the zero: -5w = 3x Divide each side by '-5'. w = -0.6x Simplifying w = -0.6xSubproblem 2
Set the factor '(8w + -3x)' equal to zero and attempt to solve: Simplifying 8w + -3x = 0 Solving 8w + -3x = 0 Move all terms containing w to the left, all other terms to the right. Add '3x' to each side of the equation. 8w + -3x + 3x = 0 + 3x Combine like terms: -3x + 3x = 0 8w + 0 = 0 + 3x 8w = 0 + 3x Remove the zero: 8w = 3x Divide each side by '8'. w = 0.375x Simplifying w = 0.375xSolution
w = {-0.6x, 0.375x}
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