(x-4)*(2x+1.3)=59.4

Solution for (x-4)*(2x+1.3)=59.4 equation:

Simplifying
(x + -4)(2x + 1.3) = 59.4

Reorder the terms:
(-4 + x)(2x + 1.3) = 59.4

Reorder the terms:
(-4 + x)(1.3 + 2x) = 59.4

Multiply (-4 + x) * (1.3 + 2x)
(-4(1.3 + 2x) + x(1.3 + 2x)) = 59.4
((1.3 * -4 + 2x * -4) + x(1.3 + 2x)) = 59.4
((-5.2 + -8x) + x(1.3 + 2x)) = 59.4
(-5.2 + -8x + (1.3 * x + 2x * x)) = 59.4
(-5.2 + -8x + (1.3x + 2x2)) = 59.4

Combine like terms: -8x + 1.3x = -6.7x
(-5.2 + -6.7x + 2x2) = 59.4

Solving
-5.2 + -6.7x + 2x2 = 59.4

Solving for variable 'x'.

Reorder the terms:
-5.2 + -59.4 + -6.7x + 2x2 = 59.4 + -59.4

Combine like terms: -5.2 + -59.4 = -64.6
-64.6 + -6.7x + 2x2 = 59.4 + -59.4

Combine like terms: 59.4 + -59.4 = 0.0
-64.6 + -6.7x + 2x2 = 0.0

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

Divide each side by '2'.
-32.3 + -3.35x + x2 = 0.0

Move the constant term to the right:

Add '32.3' to each side of the equation.
-32.3 + -3.35x + 32.3 + x2 = 0.0 + 32.3

Reorder the terms:
-32.3 + 32.3 + -3.35x + x2 = 0.0 + 32.3

Combine like terms: -32.3 + 32.3 = 0.0
0.0 + -3.35x + x2 = 0.0 + 32.3
-3.35x + x2 = 0.0 + 32.3

Combine like terms: 0.0 + 32.3 = 32.3
-3.35x + x2 = 32.3

The x term is -3.35x.  Take half its coefficient (-1.675).
Square it (2.805625) and add it to both sides.

Add '2.805625' to each side of the equation.
-3.35x + 2.805625 + x2 = 32.3 + 2.805625

Reorder the terms:
2.805625 + -3.35x + x2 = 32.3 + 2.805625

Combine like terms: 32.3 + 2.805625 = 35.105625
2.805625 + -3.35x + x2 = 35.105625

Factor a perfect square on the left side:
(x + -1.675)(x + -1.675) = 35.105625

Calculate the square root of the right side: 5.925

Break this problem into two subproblems by setting 
(x + -1.675) equal to 5.925 and -5.925.

Subproblem 1
x + -1.675 = 5.925

Simplifying
x + -1.675 = 5.925

Reorder the terms:
-1.675 + x = 5.925

Solving
-1.675 + x = 5.925

Solving for variable 'x'.

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

Add '1.675' to each side of the equation.
-1.675 + 1.675 + x = 5.925 + 1.675

Combine like terms: -1.675 + 1.675 = 0.000
0.000 + x = 5.925 + 1.675
x = 5.925 + 1.675

Combine like terms: 5.925 + 1.675 = 7.6
x = 7.6

Simplifying
x = 7.6

Subproblem 2
x + -1.675 = -5.925

Simplifying
x + -1.675 = -5.925

Reorder the terms:
-1.675 + x = -5.925

Solving
-1.675 + x = -5.925

Solving for variable 'x'.

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

Add '1.675' to each side of the equation.
-1.675 + 1.675 + x = -5.925 + 1.675

Combine like terms: -1.675 + 1.675 = 0.000
0.000 + x = -5.925 + 1.675
x = -5.925 + 1.675

Combine like terms: -5.925 + 1.675 = -4.25
x = -4.25

Simplifying
x = -4.25

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.6, -4.25}