9*b^2+6*b+1=900

Solution for 9*b^2+6*b+1=900 equation:

Simplifying
9b2 + 6b + 1 = 900

Reorder the terms:
1 + 6b + 9b2 = 900

Solving
1 + 6b + 9b2 = 900

Solving for variable 'b'.

Reorder the terms:
1 + -900 + 6b + 9b2 = 900 + -900

Combine like terms: 1 + -900 = -899
-899 + 6b + 9b2 = 900 + -900

Combine like terms: 900 + -900 = 0
-899 + 6b + 9b2 = 0

Factor a trinomial.
(-31 + -3b)(29 + -3b) = 0

Subproblem 1
Set the factor '(-31 + -3b)' equal to zero and attempt to solve:

Simplifying
-31 + -3b = 0

Solving
-31 + -3b = 0

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

Add '31' to each side of the equation.
-31 + 31 + -3b = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -3b = 0 + 31
-3b = 0 + 31

Combine like terms: 0 + 31 = 31
-3b = 31

Divide each side by '-3'.
b = -10.33333333

Simplifying
b = -10.33333333
Subproblem 2
Set the factor '(29 + -3b)' equal to zero and attempt to solve:

Simplifying
29 + -3b = 0

Solving
29 + -3b = 0

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

Add '-29' to each side of the equation.
29 + -29 + -3b = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -3b = 0 + -29
-3b = 0 + -29

Combine like terms: 0 + -29 = -29
-3b = -29

Divide each side by '-3'.
b = 9.666666667

Simplifying
b = 9.666666667
Solution
b = {-10.33333333, 9.666666667}