2*(x^2)+1=2*x+13

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Solution for 2*(x^2)+1=2*x+13 equation: 


Simplifying
2(x2) + 1 = 2x + 13

Reorder the terms:
1 + 2x2 = 2x + 13

Reorder the terms:
1 + 2x2 = 13 + 2x

Solving
1 + 2x2 = 13 + 2x

Solving for variable 'x'.

Reorder the terms:
1 + -13 + -2x + 2x2 = 13 + 2x + -13 + -2x

Combine like terms: 1 + -13 = -12
-12 + -2x + 2x2 = 13 + 2x + -13 + -2x

Reorder the terms:
-12 + -2x + 2x2 = 13 + -13 + 2x + -2x

Combine like terms: 13 + -13 = 0
-12 + -2x + 2x2 = 0 + 2x + -2x
-12 + -2x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-12 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1x + x2) = 0

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

Ignore the factor 2.

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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2, 3}

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