b+6b^2-7=0

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

Simplifying
b + 6b2 + -7 = 0

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

Solving
-7 + b + 6b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-7 + -6b)(1 + -1b) = 0

Subproblem 1
Set the factor '(-7 + -6b)' equal to zero and attempt to solve:

Simplifying
-7 + -6b = 0

Solving
-7 + -6b = 0

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

Add '7' to each side of the equation.
-7 + 7 + -6b = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6b = 0 + 7
-6b = 0 + 7

Combine like terms: 0 + 7 = 7
-6b = 7

Divide each side by '-6'.
b = -1.166666667

Simplifying
b = -1.166666667
Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve:

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

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

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

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

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

Simplifying
b = 1
Solution
b = {-1.166666667, 1}