(x+.4)(x+1.5)=0

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Solution for (x+.4)(x+1.5)=0 equation:


Simplifying
(x + 0.4)(x + 1.5) = 0

Reorder the terms:
(0.4 + x)(x + 1.5) = 0

Reorder the terms:
(0.4 + x)(1.5 + x) = 0

Multiply (0.4 + x) * (1.5 + x)
(0.4(1.5 + x) + x(1.5 + x)) = 0
((1.5 * 0.4 + x * 0.4) + x(1.5 + x)) = 0
((0.6 + 0.4x) + x(1.5 + x)) = 0
(0.6 + 0.4x + (1.5 * x + x * x)) = 0
(0.6 + 0.4x + (1.5x + x2)) = 0

Combine like terms: 0.4x + 1.5x = 1.9x
(0.6 + 1.9x + x2) = 0

Solving
0.6 + 1.9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 1.9x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 1.9x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 1.9x + x2 = 0 + -0.6
1.9x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
1.9x + x2 = -0.6

The x term is 1.9x.  Take half its coefficient (0.95).
Square it (0.9025) and add it to both sides.

Add '0.9025' to each side of the equation.
1.9x + 0.9025 + x2 = -0.6 + 0.9025

Reorder the terms:
0.9025 + 1.9x + x2 = -0.6 + 0.9025

Combine like terms: -0.6 + 0.9025 = 0.3025
0.9025 + 1.9x + x2 = 0.3025

Factor a perfect square on the left side:
(x + 0.95)(x + 0.95) = 0.3025

Calculate the square root of the right side: 0.55

Break this problem into two subproblems by setting 
(x + 0.95) equal to 0.55 and -0.55.

Subproblem 1

x + 0.95 = 0.55 Simplifying x + 0.95 = 0.55 Reorder the terms: 0.95 + x = 0.55 Solving 0.95 + x = 0.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = 0.55 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = 0.55 + -0.95 x = 0.55 + -0.95 Combine like terms: 0.55 + -0.95 = -0.4 x = -0.4 Simplifying x = -0.4

Subproblem 2

x + 0.95 = -0.55 Simplifying x + 0.95 = -0.55 Reorder the terms: 0.95 + x = -0.55 Solving 0.95 + x = -0.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = -0.55 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = -0.55 + -0.95 x = -0.55 + -0.95 Combine like terms: -0.55 + -0.95 = -1.5 x = -1.5 Simplifying x = -1.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.4, -1.5}

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