2x(x-3)=3(x+4)

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Solution for 2x(x-3)=3(x+4) equation:


Simplifying
2x(x + -3) = 3(x + 4)

Reorder the terms:
2x(-3 + x) = 3(x + 4)
(-3 * 2x + x * 2x) = 3(x + 4)
(-6x + 2x2) = 3(x + 4)

Reorder the terms:
-6x + 2x2 = 3(4 + x)
-6x + 2x2 = (4 * 3 + x * 3)
-6x + 2x2 = (12 + 3x)

Solving
-6x + 2x2 = 12 + 3x

Solving for variable 'x'.

Reorder the terms:
-12 + -6x + -3x + 2x2 = 12 + 3x + -12 + -3x

Combine like terms: -6x + -3x = -9x
-12 + -9x + 2x2 = 12 + 3x + -12 + -3x

Reorder the terms:
-12 + -9x + 2x2 = 12 + -12 + 3x + -3x

Combine like terms: 12 + -12 = 0
-12 + -9x + 2x2 = 0 + 3x + -3x
-12 + -9x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-12 + -9x + 2x2 = 0

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

Divide each side by '2'.
-6 + -4.5x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -4.5x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -4.5x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -4.5x + x2 = 0 + 6
-4.5x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-4.5x + x2 = 6

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 6 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 6 + 5.0625

Combine like terms: 6 + 5.0625 = 11.0625
5.0625 + -4.5x + x2 = 11.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(x + -2.25) equal to 3.326033674 and -3.326033674.

Subproblem 1

x + -2.25 = 3.326033674 Simplifying x + -2.25 = 3.326033674 Reorder the terms: -2.25 + x = 3.326033674 Solving -2.25 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 3.326033674 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 3.326033674 + 2.25 x = 3.326033674 + 2.25 Combine like terms: 3.326033674 + 2.25 = 5.576033674 x = 5.576033674 Simplifying x = 5.576033674

Subproblem 2

x + -2.25 = -3.326033674 Simplifying x + -2.25 = -3.326033674 Reorder the terms: -2.25 + x = -3.326033674 Solving -2.25 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -3.326033674 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -3.326033674 + 2.25 x = -3.326033674 + 2.25 Combine like terms: -3.326033674 + 2.25 = -1.076033674 x = -1.076033674 Simplifying x = -1.076033674

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.576033674, -1.076033674}

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