7-x=(x-5)(x-5)

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Solution for 7-x=(x-5)(x-5) equation: 


Simplifying
7 + -1x = (x + -5)(x + -5)

Reorder the terms:
7 + -1x = (-5 + x)(x + -5)

Reorder the terms:
7 + -1x = (-5 + x)(-5 + x)

Multiply (-5 + x) * (-5 + x)
7 + -1x = (-5(-5 + x) + x(-5 + x))
7 + -1x = ((-5 * -5 + x * -5) + x(-5 + x))
7 + -1x = ((25 + -5x) + x(-5 + x))
7 + -1x = (25 + -5x + (-5 * x + x * x))
7 + -1x = (25 + -5x + (-5x + x2))

Combine like terms: -5x + -5x = -10x
7 + -1x = (25 + -10x + x2)

Solving
7 + -1x = 25 + -10x + x2

Solving for variable 'x'.

Reorder the terms:
7 + -25 + -1x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: 7 + -25 = -18
-18 + -1x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: -1x + 10x = 9x
-18 + 9x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Reorder the terms:
-18 + 9x + -1x2 = 25 + -25 + -10x + 10x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-18 + 9x + -1x2 = 0 + -10x + 10x + x2 + -1x2
-18 + 9x + -1x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
-18 + 9x + -1x2 = 0 + x2 + -1x2
-18 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + 9x + -1x2 = 0

Factor a trinomial.
(-6 + x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {6, 3}

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