6b^2+7b-90=0

Solution for 6b^2+7b-90=0 equation:

Simplifying
6b2 + 7b + -90 = 0

Reorder the terms:
-90 + 7b + 6b2 = 0

Solving
-90 + 7b + 6b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-9 + -2b)(10 + -3b) = 0

Subproblem 1
Set the factor '(-9 + -2b)' equal to zero and attempt to solve:

Simplifying
-9 + -2b = 0

Solving
-9 + -2b = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2b = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2b = 0 + 9
-2b = 0 + 9

Combine like terms: 0 + 9 = 9
-2b = 9

Divide each side by '-2'.
b = -4.5

Simplifying
b = -4.5
Subproblem 2
Set the factor '(10 + -3b)' equal to zero and attempt to solve:

Simplifying
10 + -3b = 0

Solving
10 + -3b = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3b = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3b = 0 + -10
-3b = 0 + -10

Combine like terms: 0 + -10 = -10
-3b = -10

Divide each side by '-3'.
b = 3.333333333

Simplifying
b = 3.333333333
Solution
b = {-4.5, 3.333333333}