7b=3b(b+45)

Solution for 7b=3b(b+45) equation:

Simplifying
7b = 3b(b + 45)

Reorder the terms:
7b = 3b(45 + b)
7b = (45 * 3b + b * 3b)
7b = (135b + 3b2)

Solving
7b = 135b + 3b2

Solving for variable 'b'.

Combine like terms: 7b + -135b = -128b
-128b + -3b2 = 135b + 3b2 + -135b + -3b2

Reorder the terms:
-128b + -3b2 = 135b + -135b + 3b2 + -3b2

Combine like terms: 135b + -135b = 0
-128b + -3b2 = 0 + 3b2 + -3b2
-128b + -3b2 = 3b2 + -3b2

Combine like terms: 3b2 + -3b2 = 0
-128b + -3b2 = 0

Factor out the Greatest Common Factor (GCF), '-1b'.
-1b(128 + 3b) = 0

Ignore the factor -1.
Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0
Subproblem 2
Set the factor '(128 + 3b)' equal to zero and attempt to solve:

Simplifying
128 + 3b = 0

Solving
128 + 3b = 0

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

Add '-128' to each side of the equation.
128 + -128 + 3b = 0 + -128

Combine like terms: 128 + -128 = 0
0 + 3b = 0 + -128
3b = 0 + -128

Combine like terms: 0 + -128 = -128
3b = -128

Divide each side by '3'.
b = -42.66666667

Simplifying
b = -42.66666667
Solution
b = {0, -42.66666667}