4x(x-3)=15

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


Simplifying
4x(x + -3) = 15

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

Solving
-12x + 4x2 = 15

Solving for variable 'x'.

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

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

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

Divide each side by '4'.
-3.75 + -3x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -3x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -3x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -3x + x2 = 0 + 3.75
-3x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-3x + x2 = 3.75

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 = 3.75 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 3.75 + 2.25

Combine like terms: 3.75 + 2.25 = 6
2.25 + -3x + x2 = 6

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.449489743 and -2.449489743.

Subproblem 1

x + -1.5 = 2.449489743 Simplifying x + -1.5 = 2.449489743 Reorder the terms: -1.5 + x = 2.449489743 Solving -1.5 + x = 2.449489743 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 = 2.449489743 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.449489743 + 1.5 x = 2.449489743 + 1.5 Combine like terms: 2.449489743 + 1.5 = 3.949489743 x = 3.949489743 Simplifying x = 3.949489743

Subproblem 2

x + -1.5 = -2.449489743 Simplifying x + -1.5 = -2.449489743 Reorder the terms: -1.5 + x = -2.449489743 Solving -1.5 + x = -2.449489743 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 = -2.449489743 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.449489743 + 1.5 x = -2.449489743 + 1.5 Combine like terms: -2.449489743 + 1.5 = -0.949489743 x = -0.949489743 Simplifying x = -0.949489743

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.949489743, -0.949489743}

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