(x-4)(x-4)-9=0

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Solution for (x-4)(x-4)-9=0 equation: 


Simplifying
(x + -4)(x + -4) + -9 = 0

Reorder the terms:
(-4 + x)(x + -4) + -9 = 0

Reorder the terms:
(-4 + x)(-4 + x) + -9 = 0

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

Combine like terms: -4x + -4x = -8x
(16 + -8x + x2) + -9 = 0

Reorder the terms:
16 + -9 + -8x + x2 = 0

Combine like terms: 16 + -9 = 7
7 + -8x + x2 = 0

Solving
7 + -8x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(7 + -1x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1, 7}

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