6x+8=2x^2

Solution for 6x+8=2x^2 equation:

Simplifying
6x + 8 = 2x2

Reorder the terms:
8 + 6x = 2x2

Solving
8 + 6x = 2x2

Solving for variable 'x'.

Combine like terms: 2x2 + -2x2 = 0
8 + 6x + -2x2 = 0

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

Factor a trinomial.
2((4 + -1x)(1 + x)) = 0

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
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 = {4, -1}