4x^2+14x+6=8x^2+22x-6

Solution for 4x^2+14x+6=8x^2+22x-6 equation:

Simplifying
4x2 + 14x + 6 = 8x2 + 22x + -6

Reorder the terms:
6 + 14x + 4x2 = 8x2 + 22x + -6

Reorder the terms:
6 + 14x + 4x2 = -6 + 22x + 8x2

Solving
6 + 14x + 4x2 = -6 + 22x + 8x2

Solving for variable 'x'.

Reorder the terms:
6 + 6 + 14x + -22x + 4x2 + -8x2 = -6 + 22x + 8x2 + 6 + -22x + -8x2

Combine like terms: 6 + 6 = 12
12 + 14x + -22x + 4x2 + -8x2 = -6 + 22x + 8x2 + 6 + -22x + -8x2

Combine like terms: 14x + -22x = -8x
12 + -8x + 4x2 + -8x2 = -6 + 22x + 8x2 + 6 + -22x + -8x2

Combine like terms: 4x2 + -8x2 = -4x2
12 + -8x + -4x2 = -6 + 22x + 8x2 + 6 + -22x + -8x2

Reorder the terms:
12 + -8x + -4x2 = -6 + 6 + 22x + -22x + 8x2 + -8x2

Combine like terms: -6 + 6 = 0
12 + -8x + -4x2 = 0 + 22x + -22x + 8x2 + -8x2
12 + -8x + -4x2 = 22x + -22x + 8x2 + -8x2

Combine like terms: 22x + -22x = 0
12 + -8x + -4x2 = 0 + 8x2 + -8x2
12 + -8x + -4x2 = 8x2 + -8x2

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

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

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

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