b(5b+3)-1=b^2+3(b+5)

Solution for b(5b+3)-1=b^2+3(b+5) equation:

Simplifying
b(5b + 3) + -1 = b2 + 3(b + 5)

Reorder the terms:
b(3 + 5b) + -1 = b2 + 3(b + 5)
(3 * b + 5b * b) + -1 = b2 + 3(b + 5)
(3b + 5b2) + -1 = b2 + 3(b + 5)

Reorder the terms:
-1 + 3b + 5b2 = b2 + 3(b + 5)

Reorder the terms:
-1 + 3b + 5b2 = b2 + 3(5 + b)
-1 + 3b + 5b2 = b2 + (5 * 3 + b * 3)
-1 + 3b + 5b2 = b2 + (15 + 3b)

Reorder the terms:
-1 + 3b + 5b2 = 15 + 3b + b2

Add '-3b' to each side of the equation.
-1 + 3b + -3b + 5b2 = 15 + 3b + -3b + b2

Combine like terms: 3b + -3b = 0
-1 + 0 + 5b2 = 15 + 3b + -3b + b2
-1 + 5b2 = 15 + 3b + -3b + b2

Combine like terms: 3b + -3b = 0
-1 + 5b2 = 15 + 0 + b2
-1 + 5b2 = 15 + b2

Solving
-1 + 5b2 = 15 + b2

Solving for variable 'b'.

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

Add '-1b2' to each side of the equation.
-1 + 5b2 + -1b2 = 15 + b2 + -1b2

Combine like terms: 5b2 + -1b2 = 4b2
-1 + 4b2 = 15 + b2 + -1b2

Combine like terms: b2 + -1b2 = 0
-1 + 4b2 = 15 + 0
-1 + 4b2 = 15

Add '1' to each side of the equation.
-1 + 1 + 4b2 = 15 + 1

Combine like terms: -1 + 1 = 0
0 + 4b2 = 15 + 1
4b2 = 15 + 1

Combine like terms: 15 + 1 = 16
4b2 = 16

Divide each side by '4'.
b2 = 4

Simplifying
b2 = 4

Take the square root of each side:
b = {-2, 2}