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

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


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

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

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

Multiply (7 + 13w) * (-7 + 6w)
(7(-7 + 6w) + 13w * (-7 + 6w)) = 0
((-7 * 7 + 6w * 7) + 13w * (-7 + 6w)) = 0
((-49 + 42w) + 13w * (-7 + 6w)) = 0
(-49 + 42w + (-7 * 13w + 6w * 13w)) = 0
(-49 + 42w + (-91w + 78w2)) = 0

Combine like terms: 42w + -91w = -49w
(-49 + -49w + 78w2) = 0

Solving
-49 + -49w + 78w2 = 0

Solving for variable 'w'.

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


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 '(7 + -6w)' equal to zero and attempt to solve:

Simplifying
7 + -6w = 0

Solving
7 + -6w = 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 + -6w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6w = 0 + -7
-6w = 0 + -7

Combine like terms: 0 + -7 = -7
-6w = -7

Divide each side by '-6'.
w = 1.166666667

Simplifying
w = 1.166666667
Solution
w = {-0.5384615385, 1.166666667}

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