(x-1.5)*(x+3.2)=0

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Solution for (x-1.5)*(x+3.2)=0 equation: 


Simplifying
(x + -1.5)(x + 3.2) = 0

Reorder the terms:
(-1.5 + x)(x + 3.2) = 0

Reorder the terms:
(-1.5 + x)(3.2 + x) = 0

Multiply (-1.5 + x) * (3.2 + x)
(-1.5(3.2 + x) + x(3.2 + x)) = 0
((3.2 * -1.5 + x * -1.5) + x(3.2 + x)) = 0
((-4.8 + -1.5x) + x(3.2 + x)) = 0
(-4.8 + -1.5x + (3.2 * x + x * x)) = 0
(-4.8 + -1.5x + (3.2x + x2)) = 0

Combine like terms: -1.5x + 3.2x = 1.7x
(-4.8 + 1.7x + x2) = 0

Solving
-4.8 + 1.7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4.8' to each side of the equation.
-4.8 + 1.7x + 4.8 + x2 = 0 + 4.8

Reorder the terms:
-4.8 + 4.8 + 1.7x + x2 = 0 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + 1.7x + x2 = 0 + 4.8
1.7x + x2 = 0 + 4.8

Combine like terms: 0 + 4.8 = 4.8
1.7x + x2 = 4.8

The x term is 1.7x.  Take half its coefficient (0.85).
Square it (0.7225) and add it to both sides.

Add '0.7225' to each side of the equation.
1.7x + 0.7225 + x2 = 4.8 + 0.7225

Reorder the terms:
0.7225 + 1.7x + x2 = 4.8 + 0.7225

Combine like terms: 4.8 + 0.7225 = 5.5225
0.7225 + 1.7x + x2 = 5.5225

Factor a perfect square on the left side:
(x + 0.85)(x + 0.85) = 5.5225

Calculate the square root of the right side: 2.35

Break this problem into two subproblems by setting 
(x + 0.85) equal to 2.35 and -2.35.


Subproblem 1
x + 0.85 = 2.35

Simplifying
x + 0.85 = 2.35

Reorder the terms:
0.85 + x = 2.35

Solving
0.85 + x = 2.35

Solving for variable 'x'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + x = 2.35 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + x = 2.35 + -0.85
x = 2.35 + -0.85

Combine like terms: 2.35 + -0.85 = 1.5
x = 1.5

Simplifying
x = 1.5


Subproblem 2
x + 0.85 = -2.35

Simplifying
x + 0.85 = -2.35

Reorder the terms:
0.85 + x = -2.35

Solving
0.85 + x = -2.35

Solving for variable 'x'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + x = -2.35 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + x = -2.35 + -0.85
x = -2.35 + -0.85

Combine like terms: -2.35 + -0.85 = -3.2
x = -3.2

Simplifying
x = -3.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, -3.2}

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