5w^2-15w+12=2

Solution for 5w^2-15w+12=2 equation:

Simplifying
5w2 + -15w + 12 = 2

Reorder the terms:
12 + -15w + 5w2 = 2

Solving
12 + -15w + 5w2 = 2

Solving for variable 'w'.

Reorder the terms:
12 + -2 + -15w + 5w2 = 2 + -2

Combine like terms: 12 + -2 = 10
10 + -15w + 5w2 = 2 + -2

Combine like terms: 2 + -2 = 0
10 + -15w + 5w2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -3w + w2) = 0

Factor a trinomial.
5((1 + -1w)(2 + -1w)) = 0

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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

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

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

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

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {1, 2}