(4x-3)(4x-3)-64=0

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Solution for (4x-3)(4x-3)-64=0 equation:


Simplifying
(4x + -3)(4x + -3) + -64 = 0

Reorder the terms:
(-3 + 4x)(4x + -3) + -64 = 0

Reorder the terms:
(-3 + 4x)(-3 + 4x) + -64 = 0

Multiply (-3 + 4x) * (-3 + 4x)
(-3(-3 + 4x) + 4x * (-3 + 4x)) + -64 = 0
((-3 * -3 + 4x * -3) + 4x * (-3 + 4x)) + -64 = 0
((9 + -12x) + 4x * (-3 + 4x)) + -64 = 0
(9 + -12x + (-3 * 4x + 4x * 4x)) + -64 = 0
(9 + -12x + (-12x + 16x2)) + -64 = 0

Combine like terms: -12x + -12x = -24x
(9 + -24x + 16x2) + -64 = 0

Reorder the terms:
9 + -64 + -24x + 16x2 = 0

Combine like terms: 9 + -64 = -55
-55 + -24x + 16x2 = 0

Solving
-55 + -24x + 16x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -4x)(11 + -4x) = 0


Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 2
Set the factor '(11 + -4x)' equal to zero and attempt to solve:

Simplifying
11 + -4x = 0

Solving
11 + -4x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -4x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4x = 0 + -11
-4x = 0 + -11

Combine like terms: 0 + -11 = -11
-4x = -11

Divide each side by '-4'.
x = 2.75

Simplifying
x = 2.75
Solution
x = {-1.25, 2.75}

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