5x-12=3x(x+2)

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Solution for 5x-12=3x(x+2) equation: 


Simplifying
5x + -12 = 3x(x + 2)

Reorder the terms:
-12 + 5x = 3x(x + 2)

Reorder the terms:
-12 + 5x = 3x(2 + x)
-12 + 5x = (2 * 3x + x * 3x)
-12 + 5x = (6x + 3x2)

Solving
-12 + 5x = 6x + 3x2

Solving for variable 'x'.

Combine like terms: 5x + -6x = -1x
-12 + -1x + -3x2 = 6x + 3x2 + -6x + -3x2

Reorder the terms:
-12 + -1x + -3x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
-12 + -1x + -3x2 = 0 + 3x2 + -3x2
-12 + -1x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-12 + -1x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(12 + x + 3x2)' equal to zero and attempt to solve:

Simplifying
12 + x + 3x2 = 0

Solving
12 + x + 3x2 = 0

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

Divide each side by '3'.
4 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 0.3333333333x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 0.3333333333x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 0.3333333333x + x2 = 0 + -4
0.3333333333x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
0.3333333333x + x2 = -4

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.
0.3333333333x + 0.25 + x2 = -4 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = -4 + 0.25

Combine like terms: -4 + 0.25 = -3.75
0.25 + 0.3333333333x + x2 = -3.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -3.75

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.

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