(3x+5)(2x-25)=180

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Solution for (3x+5)(2x-25)=180 equation:


Simplifying
(3x + 5)(2x + -25) = 180

Reorder the terms:
(5 + 3x)(2x + -25) = 180

Reorder the terms:
(5 + 3x)(-25 + 2x) = 180

Multiply (5 + 3x) * (-25 + 2x)
(5(-25 + 2x) + 3x * (-25 + 2x)) = 180
((-25 * 5 + 2x * 5) + 3x * (-25 + 2x)) = 180
((-125 + 10x) + 3x * (-25 + 2x)) = 180
(-125 + 10x + (-25 * 3x + 2x * 3x)) = 180
(-125 + 10x + (-75x + 6x2)) = 180

Combine like terms: 10x + -75x = -65x
(-125 + -65x + 6x2) = 180

Solving
-125 + -65x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-125 + -180 + -65x + 6x2 = 180 + -180

Combine like terms: -125 + -180 = -305
-305 + -65x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-305 + -65x + 6x2 = 0

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

Divide each side by '6'.
-50.83333333 + -10.83333333x + x2 = 0

Move the constant term to the right:

Add '50.83333333' to each side of the equation.
-50.83333333 + -10.83333333x + 50.83333333 + x2 = 0 + 50.83333333

Reorder the terms:
-50.83333333 + 50.83333333 + -10.83333333x + x2 = 0 + 50.83333333

Combine like terms: -50.83333333 + 50.83333333 = 0.00000000
0.00000000 + -10.83333333x + x2 = 0 + 50.83333333
-10.83333333x + x2 = 0 + 50.83333333

Combine like terms: 0 + 50.83333333 = 50.83333333
-10.83333333x + x2 = 50.83333333

The x term is -10.83333333x.  Take half its coefficient (-5.416666665).
Square it (29.34027776) and add it to both sides.

Add '29.34027776' to each side of the equation.
-10.83333333x + 29.34027776 + x2 = 50.83333333 + 29.34027776

Reorder the terms:
29.34027776 + -10.83333333x + x2 = 50.83333333 + 29.34027776

Combine like terms: 50.83333333 + 29.34027776 = 80.17361109
29.34027776 + -10.83333333x + x2 = 80.17361109

Factor a perfect square on the left side:
(x + -5.416666665)(x + -5.416666665) = 80.17361109

Calculate the square root of the right side: 8.953971805

Break this problem into two subproblems by setting 
(x + -5.416666665) equal to 8.953971805 and -8.953971805.

Subproblem 1

x + -5.416666665 = 8.953971805 Simplifying x + -5.416666665 = 8.953971805 Reorder the terms: -5.416666665 + x = 8.953971805 Solving -5.416666665 + x = 8.953971805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.416666665' to each side of the equation. -5.416666665 + 5.416666665 + x = 8.953971805 + 5.416666665 Combine like terms: -5.416666665 + 5.416666665 = 0.000000000 0.000000000 + x = 8.953971805 + 5.416666665 x = 8.953971805 + 5.416666665 Combine like terms: 8.953971805 + 5.416666665 = 14.37063847 x = 14.37063847 Simplifying x = 14.37063847

Subproblem 2

x + -5.416666665 = -8.953971805 Simplifying x + -5.416666665 = -8.953971805 Reorder the terms: -5.416666665 + x = -8.953971805 Solving -5.416666665 + x = -8.953971805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.416666665' to each side of the equation. -5.416666665 + 5.416666665 + x = -8.953971805 + 5.416666665 Combine like terms: -5.416666665 + 5.416666665 = 0.000000000 0.000000000 + x = -8.953971805 + 5.416666665 x = -8.953971805 + 5.416666665 Combine like terms: -8.953971805 + 5.416666665 = -3.53730514 x = -3.53730514 Simplifying x = -3.53730514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.37063847, -3.53730514}

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