10b^2+11b+4=3b^2

Solution for 10b^2+11b+4=3b^2 equation:

Simplifying
10b2 + 11b + 4 = 3b2

Reorder the terms:
4 + 11b + 10b2 = 3b2

Solving
4 + 11b + 10b2 = 3b2

Solving for variable 'b'.

Combine like terms: 10b2 + -3b2 = 7b2
4 + 11b + 7b2 = 3b2 + -3b2

Combine like terms: 3b2 + -3b2 = 0
4 + 11b + 7b2 = 0

Factor a trinomial.
(1 + b)(4 + 7b) = 0

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

Simplifying
1 + b = 0

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

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

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

Simplifying
b = -1
Subproblem 2
Set the factor '(4 + 7b)' equal to zero and attempt to solve:

Simplifying
4 + 7b = 0

Solving
4 + 7b = 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 + 7b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7b = 0 + -4
7b = 0 + -4

Combine like terms: 0 + -4 = -4
7b = -4

Divide each side by '7'.
b = -0.5714285714

Simplifying
b = -0.5714285714
Solution
b = {-1, -0.5714285714}