12x(x+3)=15x-4

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Solution for 12x(x+3)=15x-4 equation:


Simplifying
12x(x + 3) = 15x + -4

Reorder the terms:
12x(3 + x) = 15x + -4
(3 * 12x + x * 12x) = 15x + -4
(36x + 12x2) = 15x + -4

Reorder the terms:
36x + 12x2 = -4 + 15x

Solving
36x + 12x2 = -4 + 15x

Solving for variable 'x'.

Reorder the terms:
4 + 36x + -15x + 12x2 = -4 + 15x + 4 + -15x

Combine like terms: 36x + -15x = 21x
4 + 21x + 12x2 = -4 + 15x + 4 + -15x

Reorder the terms:
4 + 21x + 12x2 = -4 + 4 + 15x + -15x

Combine like terms: -4 + 4 = 0
4 + 21x + 12x2 = 0 + 15x + -15x
4 + 21x + 12x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
4 + 21x + 12x2 = 0

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

Divide each side by '12'.
0.3333333333 + 1.75x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 1.75x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 1.75x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 1.75x + x2 = 0 + -0.3333333333
1.75x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
1.75x + x2 = -0.3333333333

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = -0.3333333333 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = -0.3333333333 + 0.765625

Combine like terms: -0.3333333333 + 0.765625 = 0.4322916667
0.765625 + 1.75x + x2 = 0.4322916667

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 0.4322916667

Calculate the square root of the right side: 0.65748891

Break this problem into two subproblems by setting 
(x + 0.875) equal to 0.65748891 and -0.65748891.

Subproblem 1

x + 0.875 = 0.65748891 Simplifying x + 0.875 = 0.65748891 Reorder the terms: 0.875 + x = 0.65748891 Solving 0.875 + x = 0.65748891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 0.65748891 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 0.65748891 + -0.875 x = 0.65748891 + -0.875 Combine like terms: 0.65748891 + -0.875 = -0.21751109 x = -0.21751109 Simplifying x = -0.21751109

Subproblem 2

x + 0.875 = -0.65748891 Simplifying x + 0.875 = -0.65748891 Reorder the terms: 0.875 + x = -0.65748891 Solving 0.875 + x = -0.65748891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -0.65748891 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -0.65748891 + -0.875 x = -0.65748891 + -0.875 Combine like terms: -0.65748891 + -0.875 = -1.53248891 x = -1.53248891 Simplifying x = -1.53248891

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.21751109, -1.53248891}

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