2x+5(3x-4)(x)=3520

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Solution for 2x+5(3x-4)(x)=3520 equation:


Simplifying
2x + 5(3x + -4)(x) = 3520

Reorder the terms:
2x + 5(-4 + 3x)(x) = 3520

Reorder the terms for easier multiplication:
2x + 5x(-4 + 3x) = 3520
2x + (-4 * 5x + 3x * 5x) = 3520
2x + (-20x + 15x2) = 3520

Combine like terms: 2x + -20x = -18x
-18x + 15x2 = 3520

Solving
-18x + 15x2 = 3520

Solving for variable 'x'.

Reorder the terms:
-3520 + -18x + 15x2 = 3520 + -3520

Combine like terms: 3520 + -3520 = 0
-3520 + -18x + 15x2 = 0

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

Divide each side by '15'.
-234.6666667 + -1.2x + x2 = 0

Move the constant term to the right:

Add '234.6666667' to each side of the equation.
-234.6666667 + -1.2x + 234.6666667 + x2 = 0 + 234.6666667

Reorder the terms:
-234.6666667 + 234.6666667 + -1.2x + x2 = 0 + 234.6666667

Combine like terms: -234.6666667 + 234.6666667 = 0.0000000
0.0000000 + -1.2x + x2 = 0 + 234.6666667
-1.2x + x2 = 0 + 234.6666667

Combine like terms: 0 + 234.6666667 = 234.6666667
-1.2x + x2 = 234.6666667

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 234.6666667 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 234.6666667 + 0.36

Combine like terms: 234.6666667 + 0.36 = 235.0266667
0.36 + -1.2x + x2 = 235.0266667

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 235.0266667

Calculate the square root of the right side: 15.330579464

Break this problem into two subproblems by setting 
(x + -0.6) equal to 15.330579464 and -15.330579464.

Subproblem 1

x + -0.6 = 15.330579464 Simplifying x + -0.6 = 15.330579464 Reorder the terms: -0.6 + x = 15.330579464 Solving -0.6 + x = 15.330579464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 15.330579464 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 15.330579464 + 0.6 x = 15.330579464 + 0.6 Combine like terms: 15.330579464 + 0.6 = 15.930579464 x = 15.930579464 Simplifying x = 15.930579464

Subproblem 2

x + -0.6 = -15.330579464 Simplifying x + -0.6 = -15.330579464 Reorder the terms: -0.6 + x = -15.330579464 Solving -0.6 + x = -15.330579464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -15.330579464 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -15.330579464 + 0.6 x = -15.330579464 + 0.6 Combine like terms: -15.330579464 + 0.6 = -14.730579464 x = -14.730579464 Simplifying x = -14.730579464

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.930579464, -14.730579464}

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