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Simplifying (3x + -2w)(3x + 7w) = 0 Reorder the terms: (-2w + 3x)(3x + 7w) = 0 Reorder the terms: (-2w + 3x)(7w + 3x) = 0 Multiply (-2w + 3x) * (7w + 3x) (-2w * (7w + 3x) + 3x * (7w + 3x)) = 0 ((7w * -2w + 3x * -2w) + 3x * (7w + 3x)) = 0 Reorder the terms: ((-6wx + -14w2) + 3x * (7w + 3x)) = 0 ((-6wx + -14w2) + 3x * (7w + 3x)) = 0 (-6wx + -14w2 + (7w * 3x + 3x * 3x)) = 0 (-6wx + -14w2 + (21wx + 9x2)) = 0 Reorder the terms: (-6wx + 21wx + -14w2 + 9x2) = 0 Combine like terms: -6wx + 21wx = 15wx (15wx + -14w2 + 9x2) = 0 Solving 15wx + -14w2 + 9x2 = 0 Solving for variable 'w'. Factor a trinomial. (-7w + -3x)(2w + -3x) = 0Subproblem 1
Set the factor '(-7w + -3x)' equal to zero and attempt to solve: Simplifying -7w + -3x = 0 Solving -7w + -3x = 0 Move all terms containing w to the left, all other terms to the right. Add '3x' to each side of the equation. -7w + -3x + 3x = 0 + 3x Combine like terms: -3x + 3x = 0 -7w + 0 = 0 + 3x -7w = 0 + 3x Remove the zero: -7w = 3x Divide each side by '-7'. w = -0.4285714286x Simplifying w = -0.4285714286xSubproblem 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 = {-0.4285714286x, 1.5x}
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