4x^2+8x-83=-6

Solution for 4x^2+8x-83=-6 equation:

Simplifying
4x2 + 8x + -83 = -6

Reorder the terms:
-83 + 8x + 4x2 = -6

Solving
-83 + 8x + 4x2 = -6

Solving for variable 'x'.

Reorder the terms:
-83 + 6 + 8x + 4x2 = -6 + 6

Combine like terms: -83 + 6 = -77
-77 + 8x + 4x2 = -6 + 6

Combine like terms: -6 + 6 = 0
-77 + 8x + 4x2 = 0

Factor a trinomial.
(-11 + -2x)(7 + -2x) = 0

Subproblem 1
Set the factor '(-11 + -2x)' equal to zero and attempt to solve:

Simplifying
-11 + -2x = 0

Solving
-11 + -2x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2x = 0 + 11
-2x = 0 + 11

Combine like terms: 0 + 11 = 11
-2x = 11

Divide each side by '-2'.
x = -5.5

Simplifying
x = -5.5
Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-5.5, 3.5}