(13w+9)(4w-12)=0

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Solution for (13w+9)(4w-12)=0 equation: 


Simplifying
(13w + 9)(4w + -12) = 0

Reorder the terms:
(9 + 13w)(4w + -12) = 0

Reorder the terms:
(9 + 13w)(-12 + 4w) = 0

Multiply (9 + 13w) * (-12 + 4w)
(9(-12 + 4w) + 13w * (-12 + 4w)) = 0
((-12 * 9 + 4w * 9) + 13w * (-12 + 4w)) = 0
((-108 + 36w) + 13w * (-12 + 4w)) = 0
(-108 + 36w + (-12 * 13w + 4w * 13w)) = 0
(-108 + 36w + (-156w + 52w2)) = 0

Combine like terms: 36w + -156w = -120w
(-108 + -120w + 52w2) = 0

Solving
-108 + -120w + 52w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-27 + -30w + 13w2) = 0

Factor a trinomial.
4((-9 + -13w)(3 + -1w)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-9 + -13w)' equal to zero and attempt to solve:

Simplifying
-9 + -13w = 0

Solving
-9 + -13w = 0

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

Add '9' to each side of the equation.
-9 + 9 + -13w = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -13w = 0 + 9
-13w = 0 + 9

Combine like terms: 0 + 9 = 9
-13w = 9

Divide each side by '-13'.
w = -0.6923076923

Simplifying
w = -0.6923076923

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 = {-0.6923076923, 3}

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