(2x*1.5)(2x+4)=26

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Solution for (2x*1.5)(2x+4)=26 equation: 


Simplifying
(2x * 1.5)(2x + 4) = 26

Reorder the terms for easier multiplication:
(2 * 1.5x)(2x + 4) = 26

Multiply 2 * 1.5
(3x)(2x + 4) = 26

Remove parenthesis around (3x)
3x(2x + 4) = 26

Reorder the terms:
3x(4 + 2x) = 26
(4 * 3x + 2x * 3x) = 26
(12x + 6x2) = 26

Solving
12x + 6x2 = 26

Solving for variable 'x'.

Reorder the terms:
-26 + 12x + 6x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-13 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-13 + 6x + 3x2 = 0

Solving
-13 + 6x + 3x2 = 0

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

Divide each side by '3'.
-4.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + 2x + 4.333333333 + x2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + 2x + x2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 4.333333333
2x + x2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
2x + x2 = 4.333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 4.333333333 + 1

Reorder the terms:
1 + 2x + x2 = 4.333333333 + 1

Combine like terms: 4.333333333 + 1 = 5.333333333
1 + 2x + x2 = 5.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 5.333333333

Calculate the square root of the right side: 2.309401077

Break this problem into two subproblems by setting 
(x + 1) equal to 2.309401077 and -2.309401077.


Subproblem 1
x + 1 = 2.309401077

Simplifying
x + 1 = 2.309401077

Reorder the terms:
1 + x = 2.309401077

Solving
1 + x = 2.309401077

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 2.309401077 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.309401077 + -1
x = 2.309401077 + -1

Combine like terms: 2.309401077 + -1 = 1.309401077
x = 1.309401077

Simplifying
x = 1.309401077


Subproblem 2
x + 1 = -2.309401077

Simplifying
x + 1 = -2.309401077

Reorder the terms:
1 + x = -2.309401077

Solving
1 + x = -2.309401077

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -2.309401077 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.309401077 + -1
x = -2.309401077 + -1

Combine like terms: -2.309401077 + -1 = -3.309401077
x = -3.309401077

Simplifying
x = -3.309401077


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.309401077, -3.309401077}
Solution
x = {1.309401077, -3.309401077}

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