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

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


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

Reorder the terms:
5x(-3 + 2x) = 8x + 3
(-3 * 5x + 2x * 5x) = 8x + 3
(-15x + 10x2) = 8x + 3

Reorder the terms:
-15x + 10x2 = 3 + 8x

Solving
-15x + 10x2 = 3 + 8x

Solving for variable 'x'.

Reorder the terms:
-3 + -15x + -8x + 10x2 = 3 + 8x + -3 + -8x

Combine like terms: -15x + -8x = -23x
-3 + -23x + 10x2 = 3 + 8x + -3 + -8x

Reorder the terms:
-3 + -23x + 10x2 = 3 + -3 + 8x + -8x

Combine like terms: 3 + -3 = 0
-3 + -23x + 10x2 = 0 + 8x + -8x
-3 + -23x + 10x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-3 + -23x + 10x2 = 0

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

Divide each side by '10'.
-0.3 + -2.3x + x2 = 0.0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + -2.3x + 0.3 + x2 = 0.0 + 0.3

Reorder the terms:
-0.3 + 0.3 + -2.3x + x2 = 0.0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + -2.3x + x2 = 0.0 + 0.3
-2.3x + x2 = 0.0 + 0.3

Combine like terms: 0.0 + 0.3 = 0.3
-2.3x + x2 = 0.3

The x term is -2.3x.  Take half its coefficient (-1.15).
Square it (1.3225) and add it to both sides.

Add '1.3225' to each side of the equation.
-2.3x + 1.3225 + x2 = 0.3 + 1.3225

Reorder the terms:
1.3225 + -2.3x + x2 = 0.3 + 1.3225

Combine like terms: 0.3 + 1.3225 = 1.6225
1.3225 + -2.3x + x2 = 1.6225

Factor a perfect square on the left side:
(x + -1.15)(x + -1.15) = 1.6225

Calculate the square root of the right side: 1.27377392

Break this problem into two subproblems by setting 
(x + -1.15) equal to 1.27377392 and -1.27377392.

Subproblem 1

x + -1.15 = 1.27377392 Simplifying x + -1.15 = 1.27377392 Reorder the terms: -1.15 + x = 1.27377392 Solving -1.15 + x = 1.27377392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = 1.27377392 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = 1.27377392 + 1.15 x = 1.27377392 + 1.15 Combine like terms: 1.27377392 + 1.15 = 2.42377392 x = 2.42377392 Simplifying x = 2.42377392

Subproblem 2

x + -1.15 = -1.27377392 Simplifying x + -1.15 = -1.27377392 Reorder the terms: -1.15 + x = -1.27377392 Solving -1.15 + x = -1.27377392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + x = -1.27377392 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + x = -1.27377392 + 1.15 x = -1.27377392 + 1.15 Combine like terms: -1.27377392 + 1.15 = -0.12377392 x = -0.12377392 Simplifying x = -0.12377392

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.42377392, -0.12377392}

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