(x+3)(2x+1)=15

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Solution for (x+3)(2x+1)=15 equation:


Simplifying
(x + 3)(2x + 1) = 15

Reorder the terms:
(3 + x)(2x + 1) = 15

Reorder the terms:
(3 + x)(1 + 2x) = 15

Multiply (3 + x) * (1 + 2x)
(3(1 + 2x) + x(1 + 2x)) = 15
((1 * 3 + 2x * 3) + x(1 + 2x)) = 15
((3 + 6x) + x(1 + 2x)) = 15
(3 + 6x + (1 * x + 2x * x)) = 15
(3 + 6x + (1x + 2x2)) = 15

Combine like terms: 6x + 1x = 7x
(3 + 7x + 2x2) = 15

Solving
3 + 7x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
3 + -15 + 7x + 2x2 = 15 + -15

Combine like terms: 3 + -15 = -12
-12 + 7x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-12 + 7x + 2x2 = 0

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

Divide each side by '2'.
-6 + 3.5x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3.5x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 3.5x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3.5x + x2 = 0 + 6
3.5x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
3.5x + x2 = 6

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 6 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 6 + 3.0625

Combine like terms: 6 + 3.0625 = 9.0625
3.0625 + 3.5x + x2 = 9.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(x + 1.75) equal to 3.010398645 and -3.010398645.

Subproblem 1

x + 1.75 = 3.010398645 Simplifying x + 1.75 = 3.010398645 Reorder the terms: 1.75 + x = 3.010398645 Solving 1.75 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 3.010398645 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.010398645 + -1.75 x = 3.010398645 + -1.75 Combine like terms: 3.010398645 + -1.75 = 1.260398645 x = 1.260398645 Simplifying x = 1.260398645

Subproblem 2

x + 1.75 = -3.010398645 Simplifying x + 1.75 = -3.010398645 Reorder the terms: 1.75 + x = -3.010398645 Solving 1.75 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -3.010398645 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.010398645 + -1.75 x = -3.010398645 + -1.75 Combine like terms: -3.010398645 + -1.75 = -4.760398645 x = -4.760398645 Simplifying x = -4.760398645

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.260398645, -4.760398645}

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