7=b(b-6)

Solution for 7=b(b-6) equation:

Simplifying
7 = b(b + -6)

Reorder the terms:
7 = b(-6 + b)
7 = (-6 * b + b * b)
7 = (-6b + b2)

Solving
7 = -6b + b2

Solving for variable 'b'.

Reorder the terms:
7 + 6b + -1b2 = -6b + 6b + b2 + -1b2

Combine like terms: -6b + 6b = 0
7 + 6b + -1b2 = 0 + b2 + -1b2
7 + 6b + -1b2 = b2 + -1b2

Combine like terms: b2 + -1b2 = 0
7 + 6b + -1b2 = 0

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

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

Simplifying
7 + -1b = 0

Solving
7 + -1b = 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 + -1b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1b = 0 + -7
-1b = 0 + -7

Combine like terms: 0 + -7 = -7
-1b = -7

Divide each side by '-1'.
b = 7

Simplifying
b = 7
Subproblem 2
Set the factor '(1 + b)' equal to zero and attempt to solve:

Simplifying
1 + b = 0

Solving
1 + b = 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 + b = 0 + -1

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

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

Simplifying
b = -1
Solution
b = {7, -1}