5(2x-1)=4x(x-15)

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Solution for 5(2x-1)=4x(x-15) equation:


Simplifying
5(2x + -1) = 4x(x + -15)

Reorder the terms:
5(-1 + 2x) = 4x(x + -15)
(-1 * 5 + 2x * 5) = 4x(x + -15)
(-5 + 10x) = 4x(x + -15)

Reorder the terms:
-5 + 10x = 4x(-15 + x)
-5 + 10x = (-15 * 4x + x * 4x)
-5 + 10x = (-60x + 4x2)

Solving
-5 + 10x = -60x + 4x2

Solving for variable 'x'.

Combine like terms: 10x + 60x = 70x
-5 + 70x + -4x2 = -60x + 4x2 + 60x + -4x2

Reorder the terms:
-5 + 70x + -4x2 = -60x + 60x + 4x2 + -4x2

Combine like terms: -60x + 60x = 0
-5 + 70x + -4x2 = 0 + 4x2 + -4x2
-5 + 70x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5 + 70x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
1.25 + -17.5x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -17.5x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -17.5x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -17.5x + x2 = 0 + -1.25
-17.5x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-17.5x + x2 = -1.25

The x term is -17.5x.  Take half its coefficient (-8.75).
Square it (76.5625) and add it to both sides.

Add '76.5625' to each side of the equation.
-17.5x + 76.5625 + x2 = -1.25 + 76.5625

Reorder the terms:
76.5625 + -17.5x + x2 = -1.25 + 76.5625

Combine like terms: -1.25 + 76.5625 = 75.3125
76.5625 + -17.5x + x2 = 75.3125

Factor a perfect square on the left side:
(x + -8.75)(x + -8.75) = 75.3125

Calculate the square root of the right side: 8.678277479

Break this problem into two subproblems by setting 
(x + -8.75) equal to 8.678277479 and -8.678277479.

Subproblem 1

x + -8.75 = 8.678277479 Simplifying x + -8.75 = 8.678277479 Reorder the terms: -8.75 + x = 8.678277479 Solving -8.75 + x = 8.678277479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = 8.678277479 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 8.678277479 + 8.75 x = 8.678277479 + 8.75 Combine like terms: 8.678277479 + 8.75 = 17.428277479 x = 17.428277479 Simplifying x = 17.428277479

Subproblem 2

x + -8.75 = -8.678277479 Simplifying x + -8.75 = -8.678277479 Reorder the terms: -8.75 + x = -8.678277479 Solving -8.75 + x = -8.678277479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = -8.678277479 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -8.678277479 + 8.75 x = -8.678277479 + 8.75 Combine like terms: -8.678277479 + 8.75 = 0.071722521 x = 0.071722521 Simplifying x = 0.071722521

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.428277479, 0.071722521}

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