3b(b-4)=6(b-8)

Solution for 3b(b-4)=6(b-8) equation:

Simplifying
3b(b + -4) = 6(b + -8)

Reorder the terms:
3b(-4 + b) = 6(b + -8)
(-4 * 3b + b * 3b) = 6(b + -8)
(-12b + 3b2) = 6(b + -8)

Reorder the terms:
-12b + 3b2 = 6(-8 + b)
-12b + 3b2 = (-8 * 6 + b * 6)
-12b + 3b2 = (-48 + 6b)

Solving
-12b + 3b2 = -48 + 6b

Solving for variable 'b'.

Reorder the terms:
48 + -12b + -6b + 3b2 = -48 + 6b + 48 + -6b

Combine like terms: -12b + -6b = -18b
48 + -18b + 3b2 = -48 + 6b + 48 + -6b

Reorder the terms:
48 + -18b + 3b2 = -48 + 48 + 6b + -6b

Combine like terms: -48 + 48 = 0
48 + -18b + 3b2 = 0 + 6b + -6b
48 + -18b + 3b2 = 6b + -6b

Combine like terms: 6b + -6b = 0
48 + -18b + 3b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + -6b + b2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(16 + -6b + b2)' equal to zero and attempt to solve:

Simplifying
16 + -6b + b2 = 0

Solving
16 + -6b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -6b + -16 + b2 = 0 + -16

Reorder the terms:
16 + -16 + -6b + b2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -6b + b2 = 0 + -16
-6b + b2 = 0 + -16

Combine like terms: 0 + -16 = -16
-6b + b2 = -16

The b term is -6b.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6b + 9 + b2 = -16 + 9

Reorder the terms:
9 + -6b + b2 = -16 + 9

Combine like terms: -16 + 9 = -7
9 + -6b + b2 = -7

Factor a perfect square on the left side:
(b + -3)(b + -3) = -7

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.