2(4x+-1)*-3(x+-2)=14

Solution for 2(4x+-1)*-3(x+-2)=14 equation:

Simplifying
2(4x + -1) * -3(x + -2) = 14

Reorder the terms:
2(-1 + 4x) * -3(x + -2) = 14

Reorder the terms:
2(-1 + 4x) * -3(-2 + x) = 14

Reorder the terms for easier multiplication:
2 * -3(-1 + 4x)(-2 + x) = 14

Multiply 2 * -3
-6(-1 + 4x)(-2 + x) = 14

Multiply (-1 + 4x) * (-2 + x)
-6(-1(-2 + x) + 4x * (-2 + x)) = 14
-6((-2 * -1 + x * -1) + 4x * (-2 + x)) = 14
-6((2 + -1x) + 4x * (-2 + x)) = 14
-6(2 + -1x + (-2 * 4x + x * 4x)) = 14
-6(2 + -1x + (-8x + 4x2)) = 14

Combine like terms: -1x + -8x = -9x
-6(2 + -9x + 4x2) = 14
(2 * -6 + -9x * -6 + 4x2 * -6) = 14
(-12 + 54x + -24x2) = 14

Solving
-12 + 54x + -24x2 = 14

Solving for variable 'x'.

Reorder the terms:
-12 + -14 + 54x + -24x2 = 14 + -14

Combine like terms: -12 + -14 = -26
-26 + 54x + -24x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-26 + 54x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 27x + -12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + 27x + -12x2)' equal to zero and attempt to solve:

Simplifying
-13 + 27x + -12x2 = 0

Solving
-13 + 27x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
1.083333333 + -2.25x + x2 = 0

Move the constant term to the right:

Add '-1.083333333' to each side of the equation.
1.083333333 + -2.25x + -1.083333333 + x2 = 0 + -1.083333333

Reorder the terms:
1.083333333 + -1.083333333 + -2.25x + x2 = 0 + -1.083333333

Combine like terms: 1.083333333 + -1.083333333 = 0.000000000
0.000000000 + -2.25x + x2 = 0 + -1.083333333
-2.25x + x2 = 0 + -1.083333333

Combine like terms: 0 + -1.083333333 = -1.083333333
-2.25x + x2 = -1.083333333

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = -1.083333333 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -1.083333333 + 1.265625

Combine like terms: -1.083333333 + 1.265625 = 0.182291667
1.265625 + -2.25x + x2 = 0.182291667

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 0.182291667

Calculate the square root of the right side: 0.426956282

Break this problem into two subproblems by setting 
(x + -1.125) equal to 0.426956282 and -0.426956282.

Subproblem 1
x + -1.125 = 0.426956282

Simplifying
x + -1.125 = 0.426956282

Reorder the terms:
-1.125 + x = 0.426956282

Solving
-1.125 + x = 0.426956282

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 0.426956282 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 0.426956282 + 1.125
x = 0.426956282 + 1.125

Combine like terms: 0.426956282 + 1.125 = 1.551956282
x = 1.551956282

Simplifying
x = 1.551956282

Subproblem 2
x + -1.125 = -0.426956282

Simplifying
x + -1.125 = -0.426956282

Reorder the terms:
-1.125 + x = -0.426956282

Solving
-1.125 + x = -0.426956282

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -0.426956282 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -0.426956282 + 1.125
x = -0.426956282 + 1.125

Combine like terms: -0.426956282 + 1.125 = 0.698043718
x = 0.698043718

Simplifying
x = 0.698043718

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.551956282, 0.698043718}
Solution
x = {1.551956282, 0.698043718}