4x(3x-4)+3(-2x-2)=86

Solution for 4x(3x-4)+3(-2x-2)=86 equation:

Simplifying
4x(3x + -4) + 3(-2x + -2) = 86

Reorder the terms:
4x(-4 + 3x) + 3(-2x + -2) = 86
(-4 * 4x + 3x * 4x) + 3(-2x + -2) = 86
(-16x + 12x2) + 3(-2x + -2) = 86

Reorder the terms:
-16x + 12x2 + 3(-2 + -2x) = 86
-16x + 12x2 + (-2 * 3 + -2x * 3) = 86
-16x + 12x2 + (-6 + -6x) = 86

Reorder the terms:
-6 + -16x + -6x + 12x2 = 86

Combine like terms: -16x + -6x = -22x
-6 + -22x + 12x2 = 86

Solving
-6 + -22x + 12x2 = 86

Solving for variable 'x'.

Reorder the terms:
-6 + -86 + -22x + 12x2 = 86 + -86

Combine like terms: -6 + -86 = -92
-92 + -22x + 12x2 = 86 + -86

Combine like terms: 86 + -86 = 0
-92 + -22x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-46 + -11x + 6x2) = 0

Factor a trinomial.
2((-2 + -1x)(23 + -6x)) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(23 + -6x)' equal to zero and attempt to solve:

Simplifying
23 + -6x = 0

Solving
23 + -6x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -6x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -6x = 0 + -23
-6x = 0 + -23

Combine like terms: 0 + -23 = -23
-6x = -23

Divide each side by '-6'.
x = 3.833333333

Simplifying
x = 3.833333333
Solution
x = {-2, 3.833333333}