12w^2+7w=10

Solution for 12w^2+7w=10 equation:

Simplifying
12w2 + 7w = 10

Reorder the terms:
7w + 12w2 = 10

Solving
7w + 12w2 = 10

Solving for variable 'w'.

Reorder the terms:
-10 + 7w + 12w2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 7w + 12w2 = 0

Factor a trinomial.
(-5 + -4w)(2 + -3w) = 0

Subproblem 1
Set the factor '(-5 + -4w)' equal to zero and attempt to solve:

Simplifying
-5 + -4w = 0

Solving
-5 + -4w = 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 + -4w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4w = 0 + 5
-4w = 0 + 5

Combine like terms: 0 + 5 = 5
-4w = 5

Divide each side by '-4'.
w = -1.25

Simplifying
w = -1.25
Subproblem 2
Set the factor '(2 + -3w)' equal to zero and attempt to solve:

Simplifying
2 + -3w = 0

Solving
2 + -3w = 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 + -3w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3w = 0 + -2
-3w = 0 + -2

Combine like terms: 0 + -2 = -2
-3w = -2

Divide each side by '-3'.
w = 0.6666666667

Simplifying
w = 0.6666666667
Solution
w = {-1.25, 0.6666666667}