x^2+5=(3-x)(3-x)

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Solution for x^2+5=(3-x)(3-x) equation: 


Simplifying
x2 + 5 = (3 + -1x)(3 + -1x)

Reorder the terms:
5 + x2 = (3 + -1x)(3 + -1x)

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

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

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

Solving for variable 'x'.

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

Combine like terms: 5 + -9 = -4
-4 + 6x + x2 + -1x2 = 9 + -6x + 1x2 + -9 + 6x + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 6x + 0 = 9 + -6x + 1x2 + -9 + 6x + -1x2
-4 + 6x = 9 + -6x + 1x2 + -9 + 6x + -1x2

Reorder the terms:
-4 + 6x = 9 + -9 + -6x + 6x + 1x2 + -1x2

Combine like terms: 9 + -9 = 0
-4 + 6x = 0 + -6x + 6x + 1x2 + -1x2
-4 + 6x = -6x + 6x + 1x2 + -1x2

Combine like terms: -6x + 6x = 0
-4 + 6x = 0 + 1x2 + -1x2
-4 + 6x = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-4 + 6x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3x) = 0

Ignore the factor 2.

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

Simplifying
-2 + 3x = 0

Solving
-2 + 3x = 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 + 3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x = 0 + 2
3x = 0 + 2

Combine like terms: 0 + 2 = 2
3x = 2

Divide each side by '3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {0.6666666667}

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