8b^2-6b+3=5b^2

Solution for 8b^2-6b+3=5b^2 equation:

Simplifying
8b2 + -6b + 3 = 5b2

Reorder the terms:
3 + -6b + 8b2 = 5b2

Solving
3 + -6b + 8b2 = 5b2

Solving for variable 'b'.

Combine like terms: 8b2 + -5b2 = 3b2
3 + -6b + 3b2 = 5b2 + -5b2

Combine like terms: 5b2 + -5b2 = 0
3 + -6b + 3b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -2b + b2) = 0

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

Ignore the factor 3.
Subproblem 1
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
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, 1}