(12w+7)(5w-15)=0

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Solution for (12w+7)(5w-15)=0 equation: 


Simplifying
(12w + 7)(5w + -15) = 0

Reorder the terms:
(7 + 12w)(5w + -15) = 0

Reorder the terms:
(7 + 12w)(-15 + 5w) = 0

Multiply (7 + 12w) * (-15 + 5w)
(7(-15 + 5w) + 12w * (-15 + 5w)) = 0
((-15 * 7 + 5w * 7) + 12w * (-15 + 5w)) = 0
((-105 + 35w) + 12w * (-15 + 5w)) = 0
(-105 + 35w + (-15 * 12w + 5w * 12w)) = 0
(-105 + 35w + (-180w + 60w2)) = 0

Combine like terms: 35w + -180w = -145w
(-105 + -145w + 60w2) = 0

Solving
-105 + -145w + 60w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -29w + 12w2) = 0

Factor a trinomial.
5((-7 + -12w)(3 + -1w)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -12w)' equal to zero and attempt to solve:

Simplifying
-7 + -12w = 0

Solving
-7 + -12w = 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 + -12w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12w = 0 + 7
-12w = 0 + 7

Combine like terms: 0 + 7 = 7
-12w = 7

Divide each side by '-12'.
w = -0.5833333333

Simplifying
w = -0.5833333333

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 = {-0.5833333333, 3}

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