4b^2-9b+4=-b^2

Solution for 4b^2-9b+4=-b^2 equation:

Simplifying
4b2 + -9b + 4 = -1b2

Reorder the terms:
4 + -9b + 4b2 = -1b2

Solving
4 + -9b + 4b2 = -1b2

Solving for variable 'b'.

Combine like terms: 4b2 + b2 = 5b2
4 + -9b + 5b2 = -1b2 + b2

Combine like terms: -1b2 + b2 = 0
4 + -9b + 5b2 = 0

Factor a trinomial.
(4 + -5b)(1 + -1b) = 0

Subproblem 1
Set the factor '(4 + -5b)' equal to zero and attempt to solve:

Simplifying
4 + -5b = 0

Solving
4 + -5b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5b = 0 + -4
-5b = 0 + -4

Combine like terms: 0 + -4 = -4
-5b = -4

Divide each side by '-5'.
b = 0.8

Simplifying
b = 0.8
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 = {0.8, 1}