5x^2=x+2-x^2

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Solution for 5x^2=x+2-x^2 equation: 


Simplifying
5x2 = x + 2 + -1x2

Reorder the terms:
5x2 = 2 + x + -1x2

Solving
5x2 = 2 + x + -1x2

Solving for variable 'x'.

Reorder the terms:
-2 + -1x + 5x2 + x2 = 2 + x + -1x2 + -2 + -1x + x2

Combine like terms: 5x2 + x2 = 6x2
-2 + -1x + 6x2 = 2 + x + -1x2 + -2 + -1x + x2

Reorder the terms:
-2 + -1x + 6x2 = 2 + -2 + x + -1x + -1x2 + x2

Combine like terms: 2 + -2 = 0
-2 + -1x + 6x2 = 0 + x + -1x + -1x2 + x2
-2 + -1x + 6x2 = x + -1x + -1x2 + x2

Combine like terms: x + -1x = 0
-2 + -1x + 6x2 = 0 + -1x2 + x2
-2 + -1x + 6x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-2 + -1x + 6x2 = 0

Factor a trinomial.
(-1 + -2x)(2 + -3x) = 0


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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
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 = {-0.5, 0.6666666667}

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