(5x+6)(x-3)=6

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Solution for (5x+6)(x-3)=6 equation:


Simplifying
(5x + 6)(x + -3) = 6

Reorder the terms:
(6 + 5x)(x + -3) = 6

Reorder the terms:
(6 + 5x)(-3 + x) = 6

Multiply (6 + 5x) * (-3 + x)
(6(-3 + x) + 5x * (-3 + x)) = 6
((-3 * 6 + x * 6) + 5x * (-3 + x)) = 6
((-18 + 6x) + 5x * (-3 + x)) = 6
(-18 + 6x + (-3 * 5x + x * 5x)) = 6
(-18 + 6x + (-15x + 5x2)) = 6

Combine like terms: 6x + -15x = -9x
(-18 + -9x + 5x2) = 6

Solving
-18 + -9x + 5x2 = 6

Solving for variable 'x'.

Reorder the terms:
-18 + -6 + -9x + 5x2 = 6 + -6

Combine like terms: -18 + -6 = -24
-24 + -9x + 5x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-24 + -9x + 5x2 = 0

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

Divide each side by '5'.
-4.8 + -1.8x + x2 = 0

Move the constant term to the right:

Add '4.8' to each side of the equation.
-4.8 + -1.8x + 4.8 + x2 = 0 + 4.8

Reorder the terms:
-4.8 + 4.8 + -1.8x + x2 = 0 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + -1.8x + x2 = 0 + 4.8
-1.8x + x2 = 0 + 4.8

Combine like terms: 0 + 4.8 = 4.8
-1.8x + x2 = 4.8

The x term is -1.8x.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8x + 0.81 + x2 = 4.8 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = 4.8 + 0.81

Combine like terms: 4.8 + 0.81 = 5.61
0.81 + -1.8x + x2 = 5.61

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = 5.61

Calculate the square root of the right side: 2.368543856

Break this problem into two subproblems by setting 
(x + -0.9) equal to 2.368543856 and -2.368543856.

Subproblem 1

x + -0.9 = 2.368543856 Simplifying x + -0.9 = 2.368543856 Reorder the terms: -0.9 + x = 2.368543856 Solving -0.9 + x = 2.368543856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 2.368543856 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 2.368543856 + 0.9 x = 2.368543856 + 0.9 Combine like terms: 2.368543856 + 0.9 = 3.268543856 x = 3.268543856 Simplifying x = 3.268543856

Subproblem 2

x + -0.9 = -2.368543856 Simplifying x + -0.9 = -2.368543856 Reorder the terms: -0.9 + x = -2.368543856 Solving -0.9 + x = -2.368543856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -2.368543856 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -2.368543856 + 0.9 x = -2.368543856 + 0.9 Combine like terms: -2.368543856 + 0.9 = -1.468543856 x = -1.468543856 Simplifying x = -1.468543856

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.268543856, -1.468543856}

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