(2x-3w)(x+6w)=0

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Solution for (2x-3w)(x+6w)=0 equation:


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) = 0

Subproblem 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 = -0.1666666667x

Subproblem 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 = 0.6666666667x

Solution

w = {-0.1666666667x, 0.6666666667x}

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