(x-4)(x-10)+9=0

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Solution for (x-4)(x-10)+9=0 equation: 


Simplifying
(x + -4)(x + -10) + 9 = 0

Reorder the terms:
(-4 + x)(x + -10) + 9 = 0

Reorder the terms:
(-4 + x)(-10 + x) + 9 = 0

Multiply (-4 + x) * (-10 + x)
(-4(-10 + x) + x(-10 + x)) + 9 = 0
((-10 * -4 + x * -4) + x(-10 + x)) + 9 = 0
((40 + -4x) + x(-10 + x)) + 9 = 0
(40 + -4x + (-10 * x + x * x)) + 9 = 0
(40 + -4x + (-10x + x2)) + 9 = 0

Combine like terms: -4x + -10x = -14x
(40 + -14x + x2) + 9 = 0

Reorder the terms:
40 + 9 + -14x + x2 = 0

Combine like terms: 40 + 9 = 49
49 + -14x + x2 = 0

Solving
49 + -14x + x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {7, 7}

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