3x(4-3x)+15x=-32

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Solution for 3x(4-3x)+15x=-32 equation:


Simplifying
3x(4 + -3x) + 15x = -32
(4 * 3x + -3x * 3x) + 15x = -32
(12x + -9x2) + 15x = -32

Reorder the terms:
12x + 15x + -9x2 = -32

Combine like terms: 12x + 15x = 27x
27x + -9x2 = -32

Solving
27x + -9x2 = -32

Solving for variable 'x'.

Reorder the terms:
32 + 27x + -9x2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + 27x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-3.555555556 + -3x + x2 = 0

Move the constant term to the right:

Add '3.555555556' to each side of the equation.
-3.555555556 + -3x + 3.555555556 + x2 = 0 + 3.555555556

Reorder the terms:
-3.555555556 + 3.555555556 + -3x + x2 = 0 + 3.555555556

Combine like terms: -3.555555556 + 3.555555556 = 0.000000000
0.000000000 + -3x + x2 = 0 + 3.555555556
-3x + x2 = 0 + 3.555555556

Combine like terms: 0 + 3.555555556 = 3.555555556
-3x + x2 = 3.555555556

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 3.555555556 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 3.555555556 + 2.25

Combine like terms: 3.555555556 + 2.25 = 5.805555556
2.25 + -3x + x2 = 5.805555556

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 5.805555556

Calculate the square root of the right side: 2.409472049

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.409472049 and -2.409472049.

Subproblem 1

x + -1.5 = 2.409472049 Simplifying x + -1.5 = 2.409472049 Reorder the terms: -1.5 + x = 2.409472049 Solving -1.5 + x = 2.409472049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.409472049 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.409472049 + 1.5 x = 2.409472049 + 1.5 Combine like terms: 2.409472049 + 1.5 = 3.909472049 x = 3.909472049 Simplifying x = 3.909472049

Subproblem 2

x + -1.5 = -2.409472049 Simplifying x + -1.5 = -2.409472049 Reorder the terms: -1.5 + x = -2.409472049 Solving -1.5 + x = -2.409472049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.409472049 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.409472049 + 1.5 x = -2.409472049 + 1.5 Combine like terms: -2.409472049 + 1.5 = -0.909472049 x = -0.909472049 Simplifying x = -0.909472049

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.909472049, -0.909472049}

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