-36b^2+114b-90=0

Solution for -36b^2+114b-90=0 equation:

Simplifying
-36b2 + 114b + -90 = 0

Reorder the terms:
-90 + 114b + -36b2 = 0

Solving
-90 + 114b + -36b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-15 + 19b + -6b2) = 0

Factor a trinomial.
6((-5 + 3b)(3 + -2b)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + 3b)' equal to zero and attempt to solve:

Simplifying
-5 + 3b = 0

Solving
-5 + 3b = 0

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

Add '5' to each side of the equation.
-5 + 5 + 3b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3b = 0 + 5
3b = 0 + 5

Combine like terms: 0 + 5 = 5
3b = 5

Divide each side by '3'.
b = 1.666666667

Simplifying
b = 1.666666667
Subproblem 2
Set the factor '(3 + -2b)' equal to zero and attempt to solve:

Simplifying
3 + -2b = 0

Solving
3 + -2b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2b = 0 + -3

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

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

Divide each side by '-2'.
b = 1.5

Simplifying
b = 1.5
Solution
b = {1.666666667, 1.5}