(x+5.4)(x-3)=0

Solution for (x+5.4)(x-3)=0 equation:

Simplifying
(x + 5.4)(x + -3) = 0

Reorder the terms:
(5.4 + x)(x + -3) = 0

Reorder the terms:
(5.4 + x)(-3 + x) = 0

Multiply (5.4 + x) * (-3 + x)
(5.4(-3 + x) + x(-3 + x)) = 0
((-3 * 5.4 + x * 5.4) + x(-3 + x)) = 0
((-16.2 + 5.4x) + x(-3 + x)) = 0
(-16.2 + 5.4x + (-3 * x + x * x)) = 0
(-16.2 + 5.4x + (-3x + x2)) = 0

Combine like terms: 5.4x + -3x = 2.4x
(-16.2 + 2.4x + x2) = 0

Solving
-16.2 + 2.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16.2' to each side of the equation.
-16.2 + 2.4x + 16.2 + x2 = 0 + 16.2

Reorder the terms:
-16.2 + 16.2 + 2.4x + x2 = 0 + 16.2

Combine like terms: -16.2 + 16.2 = 0.0
0.0 + 2.4x + x2 = 0 + 16.2
2.4x + x2 = 0 + 16.2

Combine like terms: 0 + 16.2 = 16.2
2.4x + x2 = 16.2

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = 16.2 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 16.2 + 1.44

Combine like terms: 16.2 + 1.44 = 17.64
1.44 + 2.4x + x2 = 17.64

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 17.64

Calculate the square root of the right side: 4.2

Break this problem into two subproblems by setting 
(x + 1.2) equal to 4.2 and -4.2.

Subproblem 1
x + 1.2 = 4.2

Simplifying
x + 1.2 = 4.2

Reorder the terms:
1.2 + x = 4.2

Solving
1.2 + x = 4.2

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = 4.2 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = 4.2 + -1.2
x = 4.2 + -1.2

Combine like terms: 4.2 + -1.2 = 3
x = 3

Simplifying
x = 3

Subproblem 2
x + 1.2 = -4.2

Simplifying
x + 1.2 = -4.2

Reorder the terms:
1.2 + x = -4.2

Solving
1.2 + x = -4.2

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = -4.2 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = -4.2 + -1.2
x = -4.2 + -1.2

Combine like terms: -4.2 + -1.2 = -5.4
x = -5.4

Simplifying
x = -5.4

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3, -5.4}