(w+6)(w-1)+(12w+7)(w-1)=0

Solution for (w+6)(w-1)+(12w+7)(w-1)=0 equation:

Simplifying
(w + 6)(w + -1) + (12w + 7)(w + -1) = 0

Reorder the terms:
(6 + w)(w + -1) + (12w + 7)(w + -1) = 0

Reorder the terms:
(6 + w)(-1 + w) + (12w + 7)(w + -1) = 0

Multiply (6 + w) * (-1 + w)
(6(-1 + w) + w(-1 + w)) + (12w + 7)(w + -1) = 0
((-1 * 6 + w * 6) + w(-1 + w)) + (12w + 7)(w + -1) = 0
((-6 + 6w) + w(-1 + w)) + (12w + 7)(w + -1) = 0
(-6 + 6w + (-1 * w + w * w)) + (12w + 7)(w + -1) = 0
(-6 + 6w + (-1w + w2)) + (12w + 7)(w + -1) = 0

Combine like terms: 6w + -1w = 5w
(-6 + 5w + w2) + (12w + 7)(w + -1) = 0

Reorder the terms:
-6 + 5w + w2 + (7 + 12w)(w + -1) = 0

Reorder the terms:
-6 + 5w + w2 + (7 + 12w)(-1 + w) = 0

Multiply (7 + 12w) * (-1 + w)
-6 + 5w + w2 + (7(-1 + w) + 12w * (-1 + w)) = 0
-6 + 5w + w2 + ((-1 * 7 + w * 7) + 12w * (-1 + w)) = 0
-6 + 5w + w2 + ((-7 + 7w) + 12w * (-1 + w)) = 0
-6 + 5w + w2 + (-7 + 7w + (-1 * 12w + w * 12w)) = 0
-6 + 5w + w2 + (-7 + 7w + (-12w + 12w2)) = 0

Combine like terms: 7w + -12w = -5w
-6 + 5w + w2 + (-7 + -5w + 12w2) = 0

Reorder the terms:
-6 + -7 + 5w + -5w + w2 + 12w2 = 0

Combine like terms: -6 + -7 = -13
-13 + 5w + -5w + w2 + 12w2 = 0

Combine like terms: 5w + -5w = 0
-13 + 0 + w2 + 12w2 = 0
-13 + w2 + 12w2 = 0

Combine like terms: w2 + 12w2 = 13w2
-13 + 13w2 = 0

Solving
-13 + 13w2 = 0

Solving for variable 'w'.

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

Add '13' to each side of the equation.
-13 + 13 + 13w2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 13w2 = 0 + 13
13w2 = 0 + 13

Combine like terms: 0 + 13 = 13
13w2 = 13

Divide each side by '13'.
w2 = 1

Simplifying
w2 = 1

Take the square root of each side:
w = {-1, 1}