6b^2+18b-6=7b+4b^2

Solution for 6b^2+18b-6=7b+4b^2 equation:

Simplifying
6b2 + 18b + -6 = 7b + 4b2

Reorder the terms:
-6 + 18b + 6b2 = 7b + 4b2

Solving
-6 + 18b + 6b2 = 7b + 4b2

Solving for variable 'b'.

Reorder the terms:
-6 + 18b + -7b + 6b2 + -4b2 = 7b + 4b2 + -7b + -4b2

Combine like terms: 18b + -7b = 11b
-6 + 11b + 6b2 + -4b2 = 7b + 4b2 + -7b + -4b2

Combine like terms: 6b2 + -4b2 = 2b2
-6 + 11b + 2b2 = 7b + 4b2 + -7b + -4b2

Reorder the terms:
-6 + 11b + 2b2 = 7b + -7b + 4b2 + -4b2

Combine like terms: 7b + -7b = 0
-6 + 11b + 2b2 = 0 + 4b2 + -4b2
-6 + 11b + 2b2 = 4b2 + -4b2

Combine like terms: 4b2 + -4b2 = 0
-6 + 11b + 2b2 = 0

Factor a trinomial.
(-6 + -1b)(1 + -2b) = 0

Subproblem 1
Set the factor '(-6 + -1b)' equal to zero and attempt to solve:

Simplifying
-6 + -1b = 0

Solving
-6 + -1b = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1b = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1b = 0 + 6
-1b = 0 + 6

Combine like terms: 0 + 6 = 6
-1b = 6

Divide each side by '-1'.
b = -6

Simplifying
b = -6
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 = {-6, 0.5}