7b^2=-7b+42

Solution for 7b^2=-7b+42 equation:

Simplifying
7b2 = -7b + 42

Reorder the terms:
7b2 = 42 + -7b

Solving
7b2 = 42 + -7b

Solving for variable 'b'.

Reorder the terms:
-42 + 7b + 7b2 = 42 + -7b + -42 + 7b

Reorder the terms:
-42 + 7b + 7b2 = 42 + -42 + -7b + 7b

Combine like terms: 42 + -42 = 0
-42 + 7b + 7b2 = 0 + -7b + 7b
-42 + 7b + 7b2 = -7b + 7b

Combine like terms: -7b + 7b = 0
-42 + 7b + 7b2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + b + b2) = 0

Factor a trinomial.
7((-3 + -1b)(2 + -1b)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-3 + -1b)' equal to zero and attempt to solve:

Simplifying
-3 + -1b = 0

Solving
-3 + -1b = 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 + -1b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1b = 0 + 3
-1b = 0 + 3

Combine like terms: 0 + 3 = 3
-1b = 3

Divide each side by '-1'.
b = -3

Simplifying
b = -3
Subproblem 2
Set the factor '(2 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1b = 0 + -2
-1b = 0 + -2

Combine like terms: 0 + -2 = -2
-1b = -2

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Solution
b = {-3, 2}