(13w+7)(6w-18)=0

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Solution for (13w+7)(6w-18)=0 equation: 


Simplifying
(13w + 7)(6w + -18) = 0

Reorder the terms:
(7 + 13w)(6w + -18) = 0

Reorder the terms:
(7 + 13w)(-18 + 6w) = 0

Multiply (7 + 13w) * (-18 + 6w)
(7(-18 + 6w) + 13w * (-18 + 6w)) = 0
((-18 * 7 + 6w * 7) + 13w * (-18 + 6w)) = 0
((-126 + 42w) + 13w * (-18 + 6w)) = 0
(-126 + 42w + (-18 * 13w + 6w * 13w)) = 0
(-126 + 42w + (-234w + 78w2)) = 0

Combine like terms: 42w + -234w = -192w
(-126 + -192w + 78w2) = 0

Solving
-126 + -192w + 78w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + -32w + 13w2) = 0

Factor a trinomial.
6((-7 + -13w)(3 + -1w)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-7 + -13w)' equal to zero and attempt to solve:

Simplifying
-7 + -13w = 0

Solving
-7 + -13w = 0

Move all terms containing w to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -13w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -13w = 0 + 7
-13w = 0 + 7

Combine like terms: 0 + 7 = 7
-13w = 7

Divide each side by '-13'.
w = -0.5384615385

Simplifying
w = -0.5384615385

Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-0.5384615385, 3}

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