4x^2+1=2x+3

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Solution for 4x^2+1=2x+3 equation: 


Simplifying
4x2 + 1 = 2x + 3

Reorder the terms:
1 + 4x2 = 2x + 3

Reorder the terms:
1 + 4x2 = 3 + 2x

Solving
1 + 4x2 = 3 + 2x

Solving for variable 'x'.

Reorder the terms:
1 + -3 + -2x + 4x2 = 3 + 2x + -3 + -2x

Combine like terms: 1 + -3 = -2
-2 + -2x + 4x2 = 3 + 2x + -3 + -2x

Reorder the terms:
-2 + -2x + 4x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
-2 + -2x + 4x2 = 0 + 2x + -2x
-2 + -2x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-2 + -2x + 4x2 = 0

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

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

Ignore the factor 2.

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.5, 1}

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