3(5-w)(3+w)=1-(4+w)(1+3w)

Solution for 3(5-w)(3+w)=1-(4+w)(1+3w) equation:

Simplifying
3(5 + -1w)(3 + w) = 1 + -1(4 + w)(1 + 3w)

Multiply (5 + -1w) * (3 + w)
3(5(3 + w) + -1w * (3 + w)) = 1 + -1(4 + w)(1 + 3w)
3((3 * 5 + w * 5) + -1w * (3 + w)) = 1 + -1(4 + w)(1 + 3w)
3((15 + 5w) + -1w * (3 + w)) = 1 + -1(4 + w)(1 + 3w)
3(15 + 5w + (3 * -1w + w * -1w)) = 1 + -1(4 + w)(1 + 3w)
3(15 + 5w + (-3w + -1w2)) = 1 + -1(4 + w)(1 + 3w)

Combine like terms: 5w + -3w = 2w
3(15 + 2w + -1w2) = 1 + -1(4 + w)(1 + 3w)
(15 * 3 + 2w * 3 + -1w2 * 3) = 1 + -1(4 + w)(1 + 3w)
(45 + 6w + -3w2) = 1 + -1(4 + w)(1 + 3w)

Multiply (4 + w) * (1 + 3w)
45 + 6w + -3w2 = 1 + -1(4(1 + 3w) + w(1 + 3w))
45 + 6w + -3w2 = 1 + -1((1 * 4 + 3w * 4) + w(1 + 3w))
45 + 6w + -3w2 = 1 + -1((4 + 12w) + w(1 + 3w))
45 + 6w + -3w2 = 1 + -1(4 + 12w + (1 * w + 3w * w))
45 + 6w + -3w2 = 1 + -1(4 + 12w + (1w + 3w2))

Combine like terms: 12w + 1w = 13w
45 + 6w + -3w2 = 1 + -1(4 + 13w + 3w2)
45 + 6w + -3w2 = 1 + (4 * -1 + 13w * -1 + 3w2 * -1)
45 + 6w + -3w2 = 1 + (-4 + -13w + -3w2)

Combine like terms: 1 + -4 = -3
45 + 6w + -3w2 = -3 + -13w + -3w2

Add '3w2' to each side of the equation.
45 + 6w + -3w2 + 3w2 = -3 + -13w + -3w2 + 3w2

Combine like terms: -3w2 + 3w2 = 0
45 + 6w + 0 = -3 + -13w + -3w2 + 3w2
45 + 6w = -3 + -13w + -3w2 + 3w2

Combine like terms: -3w2 + 3w2 = 0
45 + 6w = -3 + -13w + 0
45 + 6w = -3 + -13w

Solving
45 + 6w = -3 + -13w

Solving for variable 'w'.

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

Add '13w' to each side of the equation.
45 + 6w + 13w = -3 + -13w + 13w

Combine like terms: 6w + 13w = 19w
45 + 19w = -3 + -13w + 13w

Combine like terms: -13w + 13w = 0
45 + 19w = -3 + 0
45 + 19w = -3

Add '-45' to each side of the equation.
45 + -45 + 19w = -3 + -45

Combine like terms: 45 + -45 = 0
0 + 19w = -3 + -45
19w = -3 + -45

Combine like terms: -3 + -45 = -48
19w = -48

Divide each side by '19'.
w = -2.526315789

Simplifying
w = -2.526315789