(2x-3)*5x=24

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Solution for (2x-3)*5x=24 equation:


Simplifying
(2x + -3) * 5x = 24

Reorder the terms:
(-3 + 2x) * 5x = 24

Reorder the terms for easier multiplication:
5x(-3 + 2x) = 24
(-3 * 5x + 2x * 5x) = 24
(-15x + 10x2) = 24

Solving
-15x + 10x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + -15x + 10x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -15x + 10x2 = 0

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

Divide each side by '10'.
-2.4 + -1.5x + x2 = 0.0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + -1.5x + 2.4 + x2 = 0.0 + 2.4

Reorder the terms:
-2.4 + 2.4 + -1.5x + x2 = 0.0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + -1.5x + x2 = 0.0 + 2.4
-1.5x + x2 = 0.0 + 2.4

Combine like terms: 0.0 + 2.4 = 2.4
-1.5x + x2 = 2.4

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 2.4 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 2.4 + 0.5625

Combine like terms: 2.4 + 0.5625 = 2.9625
0.5625 + -1.5x + x2 = 2.9625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 2.9625

Calculate the square root of the right side: 1.721191448

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.721191448 and -1.721191448.

Subproblem 1

x + -0.75 = 1.721191448 Simplifying x + -0.75 = 1.721191448 Reorder the terms: -0.75 + x = 1.721191448 Solving -0.75 + x = 1.721191448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.721191448 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.721191448 + 0.75 x = 1.721191448 + 0.75 Combine like terms: 1.721191448 + 0.75 = 2.471191448 x = 2.471191448 Simplifying x = 2.471191448

Subproblem 2

x + -0.75 = -1.721191448 Simplifying x + -0.75 = -1.721191448 Reorder the terms: -0.75 + x = -1.721191448 Solving -0.75 + x = -1.721191448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.721191448 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.721191448 + 0.75 x = -1.721191448 + 0.75 Combine like terms: -1.721191448 + 0.75 = -0.971191448 x = -0.971191448 Simplifying x = -0.971191448

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.471191448, -0.971191448}

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