4w^2+10w+5=3w^2+18w-10

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Solution for 4w^2+10w+5=3w^2+18w-10 equation: 


Simplifying
4w2 + 10w + 5 = 3w2 + 18w + -10

Reorder the terms:
5 + 10w + 4w2 = 3w2 + 18w + -10

Reorder the terms:
5 + 10w + 4w2 = -10 + 18w + 3w2

Solving
5 + 10w + 4w2 = -10 + 18w + 3w2

Solving for variable 'w'.

Reorder the terms:
5 + 10 + 10w + -18w + 4w2 + -3w2 = -10 + 18w + 3w2 + 10 + -18w + -3w2

Combine like terms: 5 + 10 = 15
15 + 10w + -18w + 4w2 + -3w2 = -10 + 18w + 3w2 + 10 + -18w + -3w2

Combine like terms: 10w + -18w = -8w
15 + -8w + 4w2 + -3w2 = -10 + 18w + 3w2 + 10 + -18w + -3w2

Combine like terms: 4w2 + -3w2 = 1w2
15 + -8w + 1w2 = -10 + 18w + 3w2 + 10 + -18w + -3w2

Reorder the terms:
15 + -8w + 1w2 = -10 + 10 + 18w + -18w + 3w2 + -3w2

Combine like terms: -10 + 10 = 0
15 + -8w + 1w2 = 0 + 18w + -18w + 3w2 + -3w2
15 + -8w + 1w2 = 18w + -18w + 3w2 + -3w2

Combine like terms: 18w + -18w = 0
15 + -8w + 1w2 = 0 + 3w2 + -3w2
15 + -8w + 1w2 = 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
15 + -8w + 1w2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {3, 5}

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