5b^2+6=-10b+1

Solution for 5b^2+6=-10b+1 equation:

Simplifying
5b2 + 6 = -10b + 1

Reorder the terms:
6 + 5b2 = -10b + 1

Reorder the terms:
6 + 5b2 = 1 + -10b

Solving
6 + 5b2 = 1 + -10b

Solving for variable 'b'.

Reorder the terms:
6 + -1 + 10b + 5b2 = 1 + -10b + -1 + 10b

Combine like terms: 6 + -1 = 5
5 + 10b + 5b2 = 1 + -10b + -1 + 10b

Reorder the terms:
5 + 10b + 5b2 = 1 + -1 + -10b + 10b

Combine like terms: 1 + -1 = 0
5 + 10b + 5b2 = 0 + -10b + 10b
5 + 10b + 5b2 = -10b + 10b

Combine like terms: -10b + 10b = 0
5 + 10b + 5b2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + 2b + b2) = 0

Factor a trinomial.
5((1 + b)(1 + b)) = 0

Ignore the factor 5.
Subproblem 1
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
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 = {-1, -1}