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

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

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

Reorder the terms:
3(-2 + x) = 4x(x + 1)
(-2 * 3 + x * 3) = 4x(x + 1)
(-6 + 3x) = 4x(x + 1)

Reorder the terms:
-6 + 3x = 4x(1 + x)
-6 + 3x = (1 * 4x + x * 4x)
-6 + 3x = (4x + 4x2)

Solving
-6 + 3x = 4x + 4x2

Solving for variable 'x'.

Combine like terms: 3x + -4x = -1x
-6 + -1x + -4x2 = 4x + 4x2 + -4x + -4x2

Reorder the terms:
-6 + -1x + -4x2 = 4x + -4x + 4x2 + -4x2

Combine like terms: 4x + -4x = 0
-6 + -1x + -4x2 = 0 + 4x2 + -4x2
-6 + -1x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6 + -1x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + x + 4x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + x + 4x2)' equal to zero and attempt to solve:

Simplifying
6 + x + 4x2 = 0

Solving
6 + x + 4x2 = 0

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

Divide each side by '4'.
1.5 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.25x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.25x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.25x + x2 = 0 + -1.5
0.25x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.25x + x2 = -1.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25x + 0.25 + x2 = -1.5 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + 0.25x + x2 = -1.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.