x-3=(5-x)(5-x)

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Solution for x-3=(5-x)(5-x) equation: 


Simplifying
x + -3 = (5 + -1x)(5 + -1x)

Reorder the terms:
-3 + x = (5 + -1x)(5 + -1x)

Multiply (5 + -1x) * (5 + -1x)
-3 + x = (5(5 + -1x) + -1x * (5 + -1x))
-3 + x = ((5 * 5 + -1x * 5) + -1x * (5 + -1x))
-3 + x = ((25 + -5x) + -1x * (5 + -1x))
-3 + x = (25 + -5x + (5 * -1x + -1x * -1x))
-3 + x = (25 + -5x + (-5x + 1x2))

Combine like terms: -5x + -5x = -10x
-3 + x = (25 + -10x + 1x2)

Solving
-3 + x = 25 + -10x + 1x2

Solving for variable 'x'.

Reorder the terms:
-3 + -25 + x + 10x + -1x2 = 25 + -10x + 1x2 + -25 + 10x + -1x2

Combine like terms: -3 + -25 = -28
-28 + x + 10x + -1x2 = 25 + -10x + 1x2 + -25 + 10x + -1x2

Combine like terms: x + 10x = 11x
-28 + 11x + -1x2 = 25 + -10x + 1x2 + -25 + 10x + -1x2

Reorder the terms:
-28 + 11x + -1x2 = 25 + -25 + -10x + 10x + 1x2 + -1x2

Combine like terms: 25 + -25 = 0
-28 + 11x + -1x2 = 0 + -10x + 10x + 1x2 + -1x2
-28 + 11x + -1x2 = -10x + 10x + 1x2 + -1x2

Combine like terms: -10x + 10x = 0
-28 + 11x + -1x2 = 0 + 1x2 + -1x2
-28 + 11x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-28 + 11x + -1x2 = 0

Factor a trinomial.
(-7 + x)(4 + -1x) = 0


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

Simplifying
-7 + x = 0

Solving
-7 + x = 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 + x = 0 + 7

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

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

Simplifying
x = 7

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {7, 4}

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