4b^2+7=-8b+4

Solution for 4b^2+7=-8b+4 equation:

Simplifying
4b2 + 7 = -8b + 4

Reorder the terms:
7 + 4b2 = -8b + 4

Reorder the terms:
7 + 4b2 = 4 + -8b

Solving
7 + 4b2 = 4 + -8b

Solving for variable 'b'.

Reorder the terms:
7 + -4 + 8b + 4b2 = 4 + -8b + -4 + 8b

Combine like terms: 7 + -4 = 3
3 + 8b + 4b2 = 4 + -8b + -4 + 8b

Reorder the terms:
3 + 8b + 4b2 = 4 + -4 + -8b + 8b

Combine like terms: 4 + -4 = 0
3 + 8b + 4b2 = 0 + -8b + 8b
3 + 8b + 4b2 = -8b + 8b

Combine like terms: -8b + 8b = 0
3 + 8b + 4b2 = 0

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

Subproblem 1
Set the factor '(3 + 2b)' equal to zero and attempt to solve:

Simplifying
3 + 2b = 0

Solving
3 + 2b = 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 + 2b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2b = 0 + -3
2b = 0 + -3

Combine like terms: 0 + -3 = -3
2b = -3

Divide each side by '2'.
b = -1.5

Simplifying
b = -1.5
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 = {-1.5, -0.5}