=(1.2-x)(1.5-x)

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Solution for =(1.2-x)(1.5-x) equation: 


Simplifying
0 = (1.2 + -1x)(1.5 + -1x)

Multiply (1.2 + -1x) * (1.5 + -1x)
0 = (1.2(1.5 + -1x) + -1x * (1.5 + -1x))
0 = ((1.5 * 1.2 + -1x * 1.2) + -1x * (1.5 + -1x))
0 = ((1.8 + -1.2x) + -1x * (1.5 + -1x))
0 = (1.8 + -1.2x + (1.5 * -1x + -1x * -1x))
0 = (1.8 + -1.2x + (-1.5x + 1x2))

Combine like terms: -1.2x + -1.5x = -2.7x
0 = (1.8 + -2.7x + 1x2)

Solving
0 = 1.8 + -2.7x + 1x2

Solving for variable 'x'.

Combine like terms: 0 + -1.8 = -1.8
-1.8 + 2.7x + -1x2 = 1.8 + -2.7x + 1x2 + -1.8 + 2.7x + -1x2

Reorder the terms:
-1.8 + 2.7x + -1x2 = 1.8 + -1.8 + -2.7x + 2.7x + 1x2 + -1x2

Combine like terms: 1.8 + -1.8 = 0.0
-1.8 + 2.7x + -1x2 = 0.0 + -2.7x + 2.7x + 1x2 + -1x2
-1.8 + 2.7x + -1x2 = -2.7x + 2.7x + 1x2 + -1x2

Combine like terms: -2.7x + 2.7x = 0.0
-1.8 + 2.7x + -1x2 = 0.0 + 1x2 + -1x2
-1.8 + 2.7x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-1.8 + 2.7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1.8 + -2.7x + x2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + -2.7x + -1.8 + x2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + -2.7x + x2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + -2.7x + x2 = 0 + -1.8
-2.7x + x2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
-2.7x + x2 = -1.8

The x term is -2.7x.  Take half its coefficient (-1.35).
Square it (1.8225) and add it to both sides.

Add '1.8225' to each side of the equation.
-2.7x + 1.8225 + x2 = -1.8 + 1.8225

Reorder the terms:
1.8225 + -2.7x + x2 = -1.8 + 1.8225

Combine like terms: -1.8 + 1.8225 = 0.0225
1.8225 + -2.7x + x2 = 0.0225

Factor a perfect square on the left side:
(x + -1.35)(x + -1.35) = 0.0225

Calculate the square root of the right side: 0.15

Break this problem into two subproblems by setting 
(x + -1.35) equal to 0.15 and -0.15.


Subproblem 1
x + -1.35 = 0.15

Simplifying
x + -1.35 = 0.15

Reorder the terms:
-1.35 + x = 0.15

Solving
-1.35 + x = 0.15

Solving for variable 'x'.

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

Add '1.35' to each side of the equation.
-1.35 + 1.35 + x = 0.15 + 1.35

Combine like terms: -1.35 + 1.35 = 0.00
0.00 + x = 0.15 + 1.35
x = 0.15 + 1.35

Combine like terms: 0.15 + 1.35 = 1.5
x = 1.5

Simplifying
x = 1.5


Subproblem 2
x + -1.35 = -0.15

Simplifying
x + -1.35 = -0.15

Reorder the terms:
-1.35 + x = -0.15

Solving
-1.35 + x = -0.15

Solving for variable 'x'.

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

Add '1.35' to each side of the equation.
-1.35 + 1.35 + x = -0.15 + 1.35

Combine like terms: -1.35 + 1.35 = 0.00
0.00 + x = -0.15 + 1.35
x = -0.15 + 1.35

Combine like terms: -0.15 + 1.35 = 1.2
x = 1.2

Simplifying
x = 1.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, 1.2}

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