3x(5x-4)=8x+2

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Solution for 3x(5x-4)=8x+2 equation:


Simplifying
3x(5x + -4) = 8x + 2

Reorder the terms:
3x(-4 + 5x) = 8x + 2
(-4 * 3x + 5x * 3x) = 8x + 2
(-12x + 15x2) = 8x + 2

Reorder the terms:
-12x + 15x2 = 2 + 8x

Solving
-12x + 15x2 = 2 + 8x

Solving for variable 'x'.

Reorder the terms:
-2 + -12x + -8x + 15x2 = 2 + 8x + -2 + -8x

Combine like terms: -12x + -8x = -20x
-2 + -20x + 15x2 = 2 + 8x + -2 + -8x

Reorder the terms:
-2 + -20x + 15x2 = 2 + -2 + 8x + -8x

Combine like terms: 2 + -2 = 0
-2 + -20x + 15x2 = 0 + 8x + -8x
-2 + -20x + 15x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-2 + -20x + 15x2 = 0

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

Divide each side by '15'.
-0.1333333333 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.1333333333' to each side of the equation.
-0.1333333333 + -1.333333333x + 0.1333333333 + x2 = 0 + 0.1333333333

Reorder the terms:
-0.1333333333 + 0.1333333333 + -1.333333333x + x2 = 0 + 0.1333333333

Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000
0.0000000000 + -1.333333333x + x2 = 0 + 0.1333333333
-1.333333333x + x2 = 0 + 0.1333333333

Combine like terms: 0 + 0.1333333333 = 0.1333333333
-1.333333333x + x2 = 0.1333333333

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 0.1333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 0.1333333333 + 0.4444444442

Combine like terms: 0.1333333333 + 0.4444444442 = 0.5777777775
0.4444444442 + -1.333333333x + x2 = 0.5777777775

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 0.5777777775

Calculate the square root of the right side: 0.76011695

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 0.76011695 and -0.76011695.

Subproblem 1

x + -0.6666666665 = 0.76011695 Simplifying x + -0.6666666665 = 0.76011695 Reorder the terms: -0.6666666665 + x = 0.76011695 Solving -0.6666666665 + x = 0.76011695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 0.76011695 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.76011695 + 0.6666666665 x = 0.76011695 + 0.6666666665 Combine like terms: 0.76011695 + 0.6666666665 = 1.4267836165 x = 1.4267836165 Simplifying x = 1.4267836165

Subproblem 2

x + -0.6666666665 = -0.76011695 Simplifying x + -0.6666666665 = -0.76011695 Reorder the terms: -0.6666666665 + x = -0.76011695 Solving -0.6666666665 + x = -0.76011695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -0.76011695 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.76011695 + 0.6666666665 x = -0.76011695 + 0.6666666665 Combine like terms: -0.76011695 + 0.6666666665 = -0.0934502835 x = -0.0934502835 Simplifying x = -0.0934502835

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.4267836165, -0.0934502835}

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