4x^2+3=6x+1

Solution for 4x^2+3=6x+1 equation:

Simplifying
4x2 + 3 = 6x + 1

Reorder the terms:
3 + 4x2 = 6x + 1

Reorder the terms:
3 + 4x2 = 1 + 6x

Solving
3 + 4x2 = 1 + 6x

Solving for variable 'x'.

Reorder the terms:
3 + -1 + -6x + 4x2 = 1 + 6x + -1 + -6x

Combine like terms: 3 + -1 = 2
2 + -6x + 4x2 = 1 + 6x + -1 + -6x

Reorder the terms:
2 + -6x + 4x2 = 1 + -1 + 6x + -6x

Combine like terms: 1 + -1 = 0
2 + -6x + 4x2 = 0 + 6x + -6x
2 + -6x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
2 + -6x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -3x + 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}