4b^2=6b+54

Solution for 4b^2=6b+54 equation:

Simplifying
4b2 = 6b + 54

Reorder the terms:
4b2 = 54 + 6b

Solving
4b2 = 54 + 6b

Solving for variable 'b'.

Reorder the terms:
-54 + -6b + 4b2 = 54 + 6b + -54 + -6b

Reorder the terms:
-54 + -6b + 4b2 = 54 + -54 + 6b + -6b

Combine like terms: 54 + -54 = 0
-54 + -6b + 4b2 = 0 + 6b + -6b
-54 + -6b + 4b2 = 6b + -6b

Combine like terms: 6b + -6b = 0
-54 + -6b + 4b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -3b + 2b2) = 0

Factor a trinomial.
2((-3 + -1b)(9 + -2b)) = 0

Ignore the factor 2.
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 '(9 + -2b)' equal to zero and attempt to solve:

Simplifying
9 + -2b = 0

Solving
9 + -2b = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2b = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2b = 0 + -9
-2b = 0 + -9

Combine like terms: 0 + -9 = -9
-2b = -9

Divide each side by '-2'.
b = 4.5

Simplifying
b = 4.5
Solution
b = {-3, 4.5}