8x+14=4x^2+2

Solution for 8x+14=4x^2+2 equation:

Simplifying
8x + 14 = 4x2 + 2

Reorder the terms:
14 + 8x = 4x2 + 2

Reorder the terms:
14 + 8x = 2 + 4x2

Solving
14 + 8x = 2 + 4x2

Solving for variable 'x'.

Reorder the terms:
14 + -2 + 8x + -4x2 = 2 + 4x2 + -2 + -4x2

Combine like terms: 14 + -2 = 12
12 + 8x + -4x2 = 2 + 4x2 + -2 + -4x2

Reorder the terms:
12 + 8x + -4x2 = 2 + -2 + 4x2 + -4x2

Combine like terms: 2 + -2 = 0
12 + 8x + -4x2 = 0 + 4x2 + -4x2
12 + 8x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12 + 8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 2x + -1x2) = 0

Factor a trinomial.
4((3 + -1x)(1 + x)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {3, -1}