(x-1.5)(x+42)=1.5

Solution for (x-1.5)(x+42)=1.5 equation:

Simplifying
(x + -1.5)(x + 42) = 1.5

Reorder the terms:
(-1.5 + x)(x + 42) = 1.5

Reorder the terms:
(-1.5 + x)(42 + x) = 1.5

Multiply (-1.5 + x) * (42 + x)
(-1.5(42 + x) + x(42 + x)) = 1.5
((42 * -1.5 + x * -1.5) + x(42 + x)) = 1.5
((-63 + -1.5x) + x(42 + x)) = 1.5
(-63 + -1.5x + (42 * x + x * x)) = 1.5
(-63 + -1.5x + (42x + x2)) = 1.5

Combine like terms: -1.5x + 42x = 40.5x
(-63 + 40.5x + x2) = 1.5

Solving
-63 + 40.5x + x2 = 1.5

Solving for variable 'x'.

Reorder the terms:
-63 + -1.5 + 40.5x + x2 = 1.5 + -1.5

Combine like terms: -63 + -1.5 = -64.5
-64.5 + 40.5x + x2 = 1.5 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
-64.5 + 40.5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '64.5' to each side of the equation.
-64.5 + 40.5x + 64.5 + x2 = 0.0 + 64.5

Reorder the terms:
-64.5 + 64.5 + 40.5x + x2 = 0.0 + 64.5

Combine like terms: -64.5 + 64.5 = 0.0
0.0 + 40.5x + x2 = 0.0 + 64.5
40.5x + x2 = 0.0 + 64.5

Combine like terms: 0.0 + 64.5 = 64.5
40.5x + x2 = 64.5

The x term is 40.5x.  Take half its coefficient (20.25).
Square it (410.0625) and add it to both sides.

Add '410.0625' to each side of the equation.
40.5x + 410.0625 + x2 = 64.5 + 410.0625

Reorder the terms:
410.0625 + 40.5x + x2 = 64.5 + 410.0625

Combine like terms: 64.5 + 410.0625 = 474.5625
410.0625 + 40.5x + x2 = 474.5625

Factor a perfect square on the left side:
(x + 20.25)(x + 20.25) = 474.5625

Calculate the square root of the right side: 21.784455467

Break this problem into two subproblems by setting 
(x + 20.25) equal to 21.784455467 and -21.784455467.

Subproblem 1
x + 20.25 = 21.784455467

Simplifying
x + 20.25 = 21.784455467

Reorder the terms:
20.25 + x = 21.784455467

Solving
20.25 + x = 21.784455467

Solving for variable 'x'.

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

Add '-20.25' to each side of the equation.
20.25 + -20.25 + x = 21.784455467 + -20.25

Combine like terms: 20.25 + -20.25 = 0.00
0.00 + x = 21.784455467 + -20.25
x = 21.784455467 + -20.25

Combine like terms: 21.784455467 + -20.25 = 1.534455467
x = 1.534455467

Simplifying
x = 1.534455467

Subproblem 2
x + 20.25 = -21.784455467

Simplifying
x + 20.25 = -21.784455467

Reorder the terms:
20.25 + x = -21.784455467

Solving
20.25 + x = -21.784455467

Solving for variable 'x'.

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

Add '-20.25' to each side of the equation.
20.25 + -20.25 + x = -21.784455467 + -20.25

Combine like terms: 20.25 + -20.25 = 0.00
0.00 + x = -21.784455467 + -20.25
x = -21.784455467 + -20.25

Combine like terms: -21.784455467 + -20.25 = -42.034455467
x = -42.034455467

Simplifying
x = -42.034455467

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.534455467, -42.034455467}