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

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


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

Reorder the terms:
3(-5 + 2x) = 5x(x + -4)
(-5 * 3 + 2x * 3) = 5x(x + -4)
(-15 + 6x) = 5x(x + -4)

Reorder the terms:
-15 + 6x = 5x(-4 + x)
-15 + 6x = (-4 * 5x + x * 5x)
-15 + 6x = (-20x + 5x2)

Solving
-15 + 6x = -20x + 5x2

Solving for variable 'x'.

Combine like terms: 6x + 20x = 26x
-15 + 26x + -5x2 = -20x + 5x2 + 20x + -5x2

Reorder the terms:
-15 + 26x + -5x2 = -20x + 20x + 5x2 + -5x2

Combine like terms: -20x + 20x = 0
-15 + 26x + -5x2 = 0 + 5x2 + -5x2
-15 + 26x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-15 + 26x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
3 + -5.2x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -5.2x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -5.2x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5.2x + x2 = 0 + -3
-5.2x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5.2x + x2 = -3

The x term is -5.2x.  Take half its coefficient (-2.6).
Square it (6.76) and add it to both sides.

Add '6.76' to each side of the equation.
-5.2x + 6.76 + x2 = -3 + 6.76

Reorder the terms:
6.76 + -5.2x + x2 = -3 + 6.76

Combine like terms: -3 + 6.76 = 3.76
6.76 + -5.2x + x2 = 3.76

Factor a perfect square on the left side:
(x + -2.6)(x + -2.6) = 3.76

Calculate the square root of the right side: 1.939071943

Break this problem into two subproblems by setting 
(x + -2.6) equal to 1.939071943 and -1.939071943.

Subproblem 1

x + -2.6 = 1.939071943 Simplifying x + -2.6 = 1.939071943 Reorder the terms: -2.6 + x = 1.939071943 Solving -2.6 + x = 1.939071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 1.939071943 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 1.939071943 + 2.6 x = 1.939071943 + 2.6 Combine like terms: 1.939071943 + 2.6 = 4.539071943 x = 4.539071943 Simplifying x = 4.539071943

Subproblem 2

x + -2.6 = -1.939071943 Simplifying x + -2.6 = -1.939071943 Reorder the terms: -2.6 + x = -1.939071943 Solving -2.6 + x = -1.939071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -1.939071943 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -1.939071943 + 2.6 x = -1.939071943 + 2.6 Combine like terms: -1.939071943 + 2.6 = 0.660928057 x = 0.660928057 Simplifying x = 0.660928057

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.539071943, 0.660928057}

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