5x(3x+2)=-5-2(7x-6)

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Solution for 5x(3x+2)=-5-2(7x-6) equation:


Simplifying
5x(3x + 2) = -5 + -2(7x + -6)

Reorder the terms:
5x(2 + 3x) = -5 + -2(7x + -6)
(2 * 5x + 3x * 5x) = -5 + -2(7x + -6)
(10x + 15x2) = -5 + -2(7x + -6)

Reorder the terms:
10x + 15x2 = -5 + -2(-6 + 7x)
10x + 15x2 = -5 + (-6 * -2 + 7x * -2)
10x + 15x2 = -5 + (12 + -14x)

Combine like terms: -5 + 12 = 7
10x + 15x2 = 7 + -14x

Solving
10x + 15x2 = 7 + -14x

Solving for variable 'x'.

Reorder the terms:
-7 + 10x + 14x + 15x2 = 7 + -14x + -7 + 14x

Combine like terms: 10x + 14x = 24x
-7 + 24x + 15x2 = 7 + -14x + -7 + 14x

Reorder the terms:
-7 + 24x + 15x2 = 7 + -7 + -14x + 14x

Combine like terms: 7 + -7 = 0
-7 + 24x + 15x2 = 0 + -14x + 14x
-7 + 24x + 15x2 = -14x + 14x

Combine like terms: -14x + 14x = 0
-7 + 24x + 15x2 = 0

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

Divide each side by '15'.
-0.4666666667 + 1.6x + x2 = 0

Move the constant term to the right:

Add '0.4666666667' to each side of the equation.
-0.4666666667 + 1.6x + 0.4666666667 + x2 = 0 + 0.4666666667

Reorder the terms:
-0.4666666667 + 0.4666666667 + 1.6x + x2 = 0 + 0.4666666667

Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000
0.0000000000 + 1.6x + x2 = 0 + 0.4666666667
1.6x + x2 = 0 + 0.4666666667

Combine like terms: 0 + 0.4666666667 = 0.4666666667
1.6x + x2 = 0.4666666667

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 0.4666666667 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 0.4666666667 + 0.64

Combine like terms: 0.4666666667 + 0.64 = 1.1066666667
0.64 + 1.6x + x2 = 1.1066666667

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 1.1066666667

Calculate the square root of the right side: 1.051982256

Break this problem into two subproblems by setting 
(x + 0.8) equal to 1.051982256 and -1.051982256.

Subproblem 1

x + 0.8 = 1.051982256 Simplifying x + 0.8 = 1.051982256 Reorder the terms: 0.8 + x = 1.051982256 Solving 0.8 + x = 1.051982256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 1.051982256 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.051982256 + -0.8 x = 1.051982256 + -0.8 Combine like terms: 1.051982256 + -0.8 = 0.251982256 x = 0.251982256 Simplifying x = 0.251982256

Subproblem 2

x + 0.8 = -1.051982256 Simplifying x + 0.8 = -1.051982256 Reorder the terms: 0.8 + x = -1.051982256 Solving 0.8 + x = -1.051982256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -1.051982256 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.051982256 + -0.8 x = -1.051982256 + -0.8 Combine like terms: -1.051982256 + -0.8 = -1.851982256 x = -1.851982256 Simplifying x = -1.851982256

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.251982256, -1.851982256}

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