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Simplifying (3x + -2w)(7x + -3w) = 0 Reorder the terms: (-2w + 3x)(7x + -3w) = 0 Reorder the terms: (-2w + 3x)(-3w + 7x) = 0 Multiply (-2w + 3x) * (-3w + 7x) (-2w * (-3w + 7x) + 3x * (-3w + 7x)) = 0 ((-3w * -2w + 7x * -2w) + 3x * (-3w + 7x)) = 0 Reorder the terms: ((-14wx + 6w2) + 3x * (-3w + 7x)) = 0 ((-14wx + 6w2) + 3x * (-3w + 7x)) = 0 (-14wx + 6w2 + (-3w * 3x + 7x * 3x)) = 0 (-14wx + 6w2 + (-9wx + 21x2)) = 0 Reorder the terms: (-14wx + -9wx + 6w2 + 21x2) = 0 Combine like terms: -14wx + -9wx = -23wx (-23wx + 6w2 + 21x2) = 0 Solving -23wx + 6w2 + 21x2 = 0 Solving for variable 'w'. Factor a trinomial. (3w + -7x)(2w + -3x) = 0Subproblem 1
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 = 2.333333333xSubproblem 2
Set the factor '(2w + -3x)' equal to zero and attempt to solve: Simplifying 2w + -3x = 0 Solving 2w + -3x = 0 Move all terms containing w to the left, all other terms to the right. Add '3x' to each side of the equation. 2w + -3x + 3x = 0 + 3x Combine like terms: -3x + 3x = 0 2w + 0 = 0 + 3x 2w = 0 + 3x Remove the zero: 2w = 3x Divide each side by '2'. w = 1.5x Simplifying w = 1.5xSolution
w = {2.333333333x, 1.5x}
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