(4x-5)(4x-5)=64

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Solution for (4x-5)(4x-5)=64 equation: 


Simplifying
(4x + -5)(4x + -5) = 64

Reorder the terms:
(-5 + 4x)(4x + -5) = 64

Reorder the terms:
(-5 + 4x)(-5 + 4x) = 64

Multiply (-5 + 4x) * (-5 + 4x)
(-5(-5 + 4x) + 4x * (-5 + 4x)) = 64
((-5 * -5 + 4x * -5) + 4x * (-5 + 4x)) = 64
((25 + -20x) + 4x * (-5 + 4x)) = 64
(25 + -20x + (-5 * 4x + 4x * 4x)) = 64
(25 + -20x + (-20x + 16x2)) = 64

Combine like terms: -20x + -20x = -40x
(25 + -40x + 16x2) = 64

Solving
25 + -40x + 16x2 = 64

Solving for variable 'x'.

Reorder the terms:
25 + -64 + -40x + 16x2 = 64 + -64

Combine like terms: 25 + -64 = -39
-39 + -40x + 16x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-39 + -40x + 16x2 = 0

Factor a trinomial.
(-3 + -4x)(13 + -4x) = 0


Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

Subproblem 2
Set the factor '(13 + -4x)' equal to zero and attempt to solve:

Simplifying
13 + -4x = 0

Solving
13 + -4x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -4x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -4x = 0 + -13
-4x = 0 + -13

Combine like terms: 0 + -13 = -13
-4x = -13

Divide each side by '-4'.
x = 3.25

Simplifying
x = 3.25
Solution
x = {-0.75, 3.25}

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