(x-.6)(2x+3)=0

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Solution for (x-.6)(2x+3)=0 equation:


Simplifying
(x + -0.6)(2x + 3) = 0

Reorder the terms:
(-0.6 + x)(2x + 3) = 0

Reorder the terms:
(-0.6 + x)(3 + 2x) = 0

Multiply (-0.6 + x) * (3 + 2x)
(-0.6(3 + 2x) + x(3 + 2x)) = 0
((3 * -0.6 + 2x * -0.6) + x(3 + 2x)) = 0
((-1.8 + -1.2x) + x(3 + 2x)) = 0
(-1.8 + -1.2x + (3 * x + 2x * x)) = 0
(-1.8 + -1.2x + (3x + 2x2)) = 0

Combine like terms: -1.2x + 3x = 1.8x
(-1.8 + 1.8x + 2x2) = 0

Solving
-1.8 + 1.8x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-0.9 + 0.9x + x2 = 0

Move the constant term to the right:

Add '0.9' to each side of the equation.
-0.9 + 0.9x + 0.9 + x2 = 0 + 0.9

Reorder the terms:
-0.9 + 0.9 + 0.9x + x2 = 0 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + 0.9x + x2 = 0 + 0.9
0.9x + x2 = 0 + 0.9

Combine like terms: 0 + 0.9 = 0.9
0.9x + x2 = 0.9

The x term is 0.9x.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9x + 0.2025 + x2 = 0.9 + 0.2025

Reorder the terms:
0.2025 + 0.9x + x2 = 0.9 + 0.2025

Combine like terms: 0.9 + 0.2025 = 1.1025
0.2025 + 0.9x + x2 = 1.1025

Factor a perfect square on the left side:
(x + 0.45)(x + 0.45) = 1.1025

Calculate the square root of the right side: 1.05

Break this problem into two subproblems by setting 
(x + 0.45) equal to 1.05 and -1.05.

Subproblem 1

x + 0.45 = 1.05 Simplifying x + 0.45 = 1.05 Reorder the terms: 0.45 + x = 1.05 Solving 0.45 + x = 1.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 1.05 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 1.05 + -0.45 x = 1.05 + -0.45 Combine like terms: 1.05 + -0.45 = 0.6 x = 0.6 Simplifying x = 0.6

Subproblem 2

x + 0.45 = -1.05 Simplifying x + 0.45 = -1.05 Reorder the terms: 0.45 + x = -1.05 Solving 0.45 + x = -1.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -1.05 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -1.05 + -0.45 x = -1.05 + -0.45 Combine like terms: -1.05 + -0.45 = -1.5 x = -1.5 Simplifying x = -1.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6, -1.5}

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