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

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Solution for 5x-1=(x-3)(x-3) equation: 


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

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

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

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

Multiply (-3 + x) * (-3 + x)
-1 + 5x = (-3(-3 + x) + x(-3 + x))
-1 + 5x = ((-3 * -3 + x * -3) + x(-3 + x))
-1 + 5x = ((9 + -3x) + x(-3 + x))
-1 + 5x = (9 + -3x + (-3 * x + x * x))
-1 + 5x = (9 + -3x + (-3x + x2))

Combine like terms: -3x + -3x = -6x
-1 + 5x = (9 + -6x + x2)

Solving
-1 + 5x = 9 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
-1 + -9 + 5x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: -1 + -9 = -10
-10 + 5x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: 5x + 6x = 11x
-10 + 11x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Reorder the terms:
-10 + 11x + -1x2 = 9 + -9 + -6x + 6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-10 + 11x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-10 + 11x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-10 + 11x + -1x2 = 0 + x2 + -1x2
-10 + 11x + -1x2 = x2 + -1x2

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

Factor a trinomial.
(-10 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10

Subproblem 2
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
Solution
x = {10, 1}

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