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Simplifying (2x + -3w)(x + 6w) = 0 Reorder the terms: (-3w + 2x)(x + 6w) = 0 Reorder the terms: (-3w + 2x)(6w + x) = 0 Multiply (-3w + 2x) * (6w + x) (-3w * (6w + x) + 2x * (6w + x)) = 0 ((6w * -3w + x * -3w) + 2x * (6w + x)) = 0 Reorder the terms: ((-3wx + -18w2) + 2x * (6w + x)) = 0 ((-3wx + -18w2) + 2x * (6w + x)) = 0 (-3wx + -18w2 + (6w * 2x + x * 2x)) = 0 (-3wx + -18w2 + (12wx + 2x2)) = 0 Reorder the terms: (-3wx + 12wx + -18w2 + 2x2) = 0 Combine like terms: -3wx + 12wx = 9wx (9wx + -18w2 + 2x2) = 0 Solving 9wx + -18w2 + 2x2 = 0 Solving for variable 'w'. Factor a trinomial. (-6w + -1x)(3w + -2x) = 0Subproblem 1
Set the factor '(-6w + -1x)' equal to zero and attempt to solve: Simplifying -6w + -1x = 0 Solving -6w + -1x = 0 Move all terms containing w to the left, all other terms to the right. Add 'x' to each side of the equation. -6w + -1x + x = 0 + x Combine like terms: -1x + x = 0 -6w + 0 = 0 + x -6w = 0 + x Remove the zero: -6w = x Divide each side by '-6'. w = -0.1666666667x Simplifying w = -0.1666666667xSubproblem 2
Set the factor '(3w + -2x)' equal to zero and attempt to solve: Simplifying 3w + -2x = 0 Solving 3w + -2x = 0 Move all terms containing w to the left, all other terms to the right. Add '2x' to each side of the equation. 3w + -2x + 2x = 0 + 2x Combine like terms: -2x + 2x = 0 3w + 0 = 0 + 2x 3w = 0 + 2x Remove the zero: 3w = 2x Divide each side by '3'. w = 0.6666666667x Simplifying w = 0.6666666667xSolution
w = {-0.1666666667x, 0.6666666667x}
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