7x^2+21x-22=6

Solution for 7x^2+21x-22=6 equation:

Simplifying
7x2 + 21x + -22 = 6

Reorder the terms:
-22 + 21x + 7x2 = 6

Solving
-22 + 21x + 7x2 = 6

Solving for variable 'x'.

Reorder the terms:
-22 + -6 + 21x + 7x2 = 6 + -6

Combine like terms: -22 + -6 = -28
-28 + 21x + 7x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-28 + 21x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-4 + 3x + x2) = 0

Factor a trinomial.
7((-4 + -1x)(1 + -1x)) = 0

Ignore the factor 7.
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 + -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 = {-4, 1}