22-2x^2=25-10x+x^2

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Solution for 22-2x^2=25-10x+x^2 equation: 


Simplifying
22 + -2x2 = 25 + -10x + x2

Solving
22 + -2x2 = 25 + -10x + x2

Solving for variable 'x'.

Reorder the terms:
22 + -25 + 10x + -2x2 + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: 22 + -25 = -3
-3 + 10x + -2x2 + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2

Combine like terms: -2x2 + -1x2 = -3x2
-3 + 10x + -3x2 = 25 + -10x + x2 + -25 + 10x + -1x2

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

Combine like terms: 25 + -25 = 0
-3 + 10x + -3x2 = 0 + -10x + 10x + x2 + -1x2
-3 + 10x + -3x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
-3 + 10x + -3x2 = 0 + x2 + -1x2
-3 + 10x + -3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + 10x + -3x2 = 0

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


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

Simplifying
-3 + x = 0

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

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

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

Simplifying
x = 3

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

Simplifying
1 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {3, 0.3333333333}

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