0=-(x-3)*(x-3)+1

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Solution for 0=-(x-3)*(x-3)+1 equation:


Simplifying
0 = -1(x + -3)(x + -3) + 1

Reorder the terms:
0 = -1(-3 + x)(x + -3) + 1

Reorder the terms:
0 = -1(-3 + x)(-3 + x) + 1

Multiply (-3 + x) * (-3 + x)
0 = -1(-3(-3 + x) + x(-3 + x)) + 1
0 = -1((-3 * -3 + x * -3) + x(-3 + x)) + 1
0 = -1((9 + -3x) + x(-3 + x)) + 1
0 = -1(9 + -3x + (-3 * x + x * x)) + 1
0 = -1(9 + -3x + (-3x + x2)) + 1

Combine like terms: -3x + -3x = -6x
0 = -1(9 + -6x + x2) + 1
0 = (9 * -1 + -6x * -1 + x2 * -1) + 1
0 = (-9 + 6x + -1x2) + 1

Reorder the terms:
0 = -9 + 1 + 6x + -1x2

Combine like terms: -9 + 1 = -8
0 = -8 + 6x + -1x2

Solving
0 = -8 + 6x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 8 = 8
8 + -6x + x2 = -8 + 6x + -1x2 + 8 + -6x + x2

Reorder the terms:
8 + -6x + x2 = -8 + 8 + 6x + -6x + -1x2 + x2

Combine like terms: -8 + 8 = 0
8 + -6x + x2 = 0 + 6x + -6x + -1x2 + x2
8 + -6x + x2 = 6x + -6x + -1x2 + x2

Combine like terms: 6x + -6x = 0
8 + -6x + x2 = 0 + -1x2 + x2
8 + -6x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
8 + -6x + x2 = 0

Factor a trinomial.
(2 + -1x)(4 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, 4}

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