10b^2+1=7b

Solution for 10b^2+1=7b equation:

Simplifying
10b2 + 1 = 7b

Reorder the terms:
1 + 10b2 = 7b

Solving
1 + 10b2 = 7b

Solving for variable 'b'.

Reorder the terms:
1 + -7b + 10b2 = 7b + -7b

Combine like terms: 7b + -7b = 0
1 + -7b + 10b2 = 0

Factor a trinomial.
(1 + -5b)(1 + -2b) = 0

Subproblem 1
Set the factor '(1 + -5b)' equal to zero and attempt to solve:

Simplifying
1 + -5b = 0

Solving
1 + -5b = 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 + -5b = 0 + -1

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

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

Divide each side by '-5'.
b = 0.2

Simplifying
b = 0.2
Subproblem 2
Set the factor '(1 + -2b)' equal to zero and attempt to solve:

Simplifying
1 + -2b = 0

Solving
1 + -2b = 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 + -2b = 0 + -1

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

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

Divide each side by '-2'.
b = 0.5

Simplifying
b = 0.5
Solution
b = {0.2, 0.5}