(4x-2)(0.6x+3)=0

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Solution for (4x-2)(0.6x+3)=0 equation: 


Simplifying
(4x + -2)(0.6x + 3) = 0

Reorder the terms:
(-2 + 4x)(0.6x + 3) = 0

Reorder the terms:
(-2 + 4x)(3 + 0.6x) = 0

Multiply (-2 + 4x) * (3 + 0.6x)
(-2(3 + 0.6x) + 4x * (3 + 0.6x)) = 0
((3 * -2 + 0.6x * -2) + 4x * (3 + 0.6x)) = 0
((-6 + -1.2x) + 4x * (3 + 0.6x)) = 0
(-6 + -1.2x + (3 * 4x + 0.6x * 4x)) = 0
(-6 + -1.2x + (12x + 2.4x2)) = 0

Combine like terms: -1.2x + 12x = 10.8x
(-6 + 10.8x + 2.4x2) = 0

Solving
-6 + 10.8x + 2.4x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.4'.
-2.5 + 4.5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 4.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 4.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 4.5x + x2 = 0 + 2.5
4.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
4.5x + x2 = 2.5

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 2.5 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 2.5 + 5.0625

Combine like terms: 2.5 + 5.0625 = 7.5625
5.0625 + 4.5x + x2 = 7.5625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 7.5625

Calculate the square root of the right side: 2.75

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.75 and -2.75.


Subproblem 1
x + 2.25 = 2.75

Simplifying
x + 2.25 = 2.75

Reorder the terms:
2.25 + x = 2.75

Solving
2.25 + x = 2.75

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 2.75 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.75 + -2.25
x = 2.75 + -2.25

Combine like terms: 2.75 + -2.25 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + 2.25 = -2.75

Simplifying
x + 2.25 = -2.75

Reorder the terms:
2.25 + x = -2.75

Solving
2.25 + x = -2.75

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -2.75 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.75 + -2.25
x = -2.75 + -2.25

Combine like terms: -2.75 + -2.25 = -5
x = -5

Simplifying
x = -5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -5}

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