(4b-3)(4b-3)=169

Solution for (4b-3)(4b-3)=169 equation:

Simplifying
(4b + -3)(4b + -3) = 169

Reorder the terms:
(-3 + 4b)(4b + -3) = 169

Reorder the terms:
(-3 + 4b)(-3 + 4b) = 169

Multiply (-3 + 4b) * (-3 + 4b)
(-3(-3 + 4b) + 4b * (-3 + 4b)) = 169
((-3 * -3 + 4b * -3) + 4b * (-3 + 4b)) = 169
((9 + -12b) + 4b * (-3 + 4b)) = 169
(9 + -12b + (-3 * 4b + 4b * 4b)) = 169
(9 + -12b + (-12b + 16b2)) = 169

Combine like terms: -12b + -12b = -24b
(9 + -24b + 16b2) = 169

Solving
9 + -24b + 16b2 = 169

Solving for variable 'b'.

Reorder the terms:
9 + -169 + -24b + 16b2 = 169 + -169

Combine like terms: 9 + -169 = -160
-160 + -24b + 16b2 = 169 + -169

Combine like terms: 169 + -169 = 0
-160 + -24b + 16b2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-20 + -3b + 2b2) = 0

Factor a trinomial.
8((-5 + -2b)(4 + -1b)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-5 + -2b)' equal to zero and attempt to solve:

Simplifying
-5 + -2b = 0

Solving
-5 + -2b = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2b = 0 + 5
-2b = 0 + 5

Combine like terms: 0 + 5 = 5
-2b = 5

Divide each side by '-2'.
b = -2.5

Simplifying
b = -2.5
Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 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 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Solution
b = {-2.5, 4}