15x(x+1)-7(x+9)=4x

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Solution for 15x(x+1)-7(x+9)=4x equation:


Simplifying
15x(x + 1) + -7(x + 9) = 4x

Reorder the terms:
15x(1 + x) + -7(x + 9) = 4x
(1 * 15x + x * 15x) + -7(x + 9) = 4x
(15x + 15x2) + -7(x + 9) = 4x

Reorder the terms:
15x + 15x2 + -7(9 + x) = 4x
15x + 15x2 + (9 * -7 + x * -7) = 4x
15x + 15x2 + (-63 + -7x) = 4x

Reorder the terms:
-63 + 15x + -7x + 15x2 = 4x

Combine like terms: 15x + -7x = 8x
-63 + 8x + 15x2 = 4x

Solving
-63 + 8x + 15x2 = 4x

Solving for variable 'x'.

Reorder the terms:
-63 + 8x + -4x + 15x2 = 4x + -4x

Combine like terms: 8x + -4x = 4x
-63 + 4x + 15x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-63 + 4x + 15x2 = 0

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

Divide each side by '15'.
-4.2 + 0.2666666667x + x2 = 0

Move the constant term to the right:

Add '4.2' to each side of the equation.
-4.2 + 0.2666666667x + 4.2 + x2 = 0 + 4.2

Reorder the terms:
-4.2 + 4.2 + 0.2666666667x + x2 = 0 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + 0.2666666667x + x2 = 0 + 4.2
0.2666666667x + x2 = 0 + 4.2

Combine like terms: 0 + 4.2 = 4.2
0.2666666667x + x2 = 4.2

The x term is 0.2666666667x.  Take half its coefficient (0.1333333334).
Square it (0.01777777780) and add it to both sides.

Add '0.01777777780' to each side of the equation.
0.2666666667x + 0.01777777780 + x2 = 4.2 + 0.01777777780

Reorder the terms:
0.01777777780 + 0.2666666667x + x2 = 4.2 + 0.01777777780

Combine like terms: 4.2 + 0.01777777780 = 4.2177777778
0.01777777780 + 0.2666666667x + x2 = 4.2177777778

Factor a perfect square on the left side:
(x + 0.1333333334)(x + 0.1333333334) = 4.2177777778

Calculate the square root of the right side: 2.053722907

Break this problem into two subproblems by setting 
(x + 0.1333333334) equal to 2.053722907 and -2.053722907.

Subproblem 1

x + 0.1333333334 = 2.053722907 Simplifying x + 0.1333333334 = 2.053722907 Reorder the terms: 0.1333333334 + x = 2.053722907 Solving 0.1333333334 + x = 2.053722907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1333333334' to each side of the equation. 0.1333333334 + -0.1333333334 + x = 2.053722907 + -0.1333333334 Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000 0.0000000000 + x = 2.053722907 + -0.1333333334 x = 2.053722907 + -0.1333333334 Combine like terms: 2.053722907 + -0.1333333334 = 1.9203895736 x = 1.9203895736 Simplifying x = 1.9203895736

Subproblem 2

x + 0.1333333334 = -2.053722907 Simplifying x + 0.1333333334 = -2.053722907 Reorder the terms: 0.1333333334 + x = -2.053722907 Solving 0.1333333334 + x = -2.053722907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1333333334' to each side of the equation. 0.1333333334 + -0.1333333334 + x = -2.053722907 + -0.1333333334 Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000 0.0000000000 + x = -2.053722907 + -0.1333333334 x = -2.053722907 + -0.1333333334 Combine like terms: -2.053722907 + -0.1333333334 = -2.1870562404 x = -2.1870562404 Simplifying x = -2.1870562404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.9203895736, -2.1870562404}

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