(x+3)(5x)+(3x-2-5)=

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Solution for (x+3)(5x)+(3x-2-5)= equation:


Simplifying
(x + 3)(5x) + (3x + -2 + -5) = 0

Reorder the terms:
(3 + x)(5x) + (3x + -2 + -5) = 0

Remove parenthesis around (5x)
(3 + x) * 5x + (3x + -2 + -5) = 0

Reorder the terms for easier multiplication:
5x(3 + x) + (3x + -2 + -5) = 0
(3 * 5x + x * 5x) + (3x + -2 + -5) = 0
(15x + 5x2) + (3x + -2 + -5) = 0

Reorder the terms:
15x + 5x2 + (-2 + -5 + 3x) = 0

Combine like terms: -2 + -5 = -7
15x + 5x2 + (-7 + 3x) = 0

Remove parenthesis around (-7 + 3x)
15x + 5x2 + -7 + 3x = 0

Reorder the terms:
-7 + 15x + 3x + 5x2 = 0

Combine like terms: 15x + 3x = 18x
-7 + 18x + 5x2 = 0

Solving
-7 + 18x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1.4 + 3.6x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 3.6x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 3.6x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 3.6x + x2 = 0 + 1.4
3.6x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
3.6x + x2 = 1.4

The x term is 3.6x.  Take half its coefficient (1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
3.6x + 3.24 + x2 = 1.4 + 3.24

Reorder the terms:
3.24 + 3.6x + x2 = 1.4 + 3.24

Combine like terms: 1.4 + 3.24 = 4.64
3.24 + 3.6x + x2 = 4.64

Factor a perfect square on the left side:
(x + 1.8)(x + 1.8) = 4.64

Calculate the square root of the right side: 2.154065923

Break this problem into two subproblems by setting 
(x + 1.8) equal to 2.154065923 and -2.154065923.

Subproblem 1

x + 1.8 = 2.154065923 Simplifying x + 1.8 = 2.154065923 Reorder the terms: 1.8 + x = 2.154065923 Solving 1.8 + x = 2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 2.154065923 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 2.154065923 + -1.8 x = 2.154065923 + -1.8 Combine like terms: 2.154065923 + -1.8 = 0.354065923 x = 0.354065923 Simplifying x = 0.354065923

Subproblem 2

x + 1.8 = -2.154065923 Simplifying x + 1.8 = -2.154065923 Reorder the terms: 1.8 + x = -2.154065923 Solving 1.8 + x = -2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -2.154065923 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -2.154065923 + -1.8 x = -2.154065923 + -1.8 Combine like terms: -2.154065923 + -1.8 = -3.954065923 x = -3.954065923 Simplifying x = -3.954065923

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.354065923, -3.954065923}

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