5(x+2)-3=3x(x-1)-9x

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Solution for 5(x+2)-3=3x(x-1)-9x equation:


Simplifying
5(x + 2) + -3 = 3x(x + -1) + -9x

Reorder the terms:
5(2 + x) + -3 = 3x(x + -1) + -9x
(2 * 5 + x * 5) + -3 = 3x(x + -1) + -9x
(10 + 5x) + -3 = 3x(x + -1) + -9x

Reorder the terms:
10 + -3 + 5x = 3x(x + -1) + -9x

Combine like terms: 10 + -3 = 7
7 + 5x = 3x(x + -1) + -9x

Reorder the terms:
7 + 5x = 3x(-1 + x) + -9x
7 + 5x = (-1 * 3x + x * 3x) + -9x
7 + 5x = (-3x + 3x2) + -9x

Reorder the terms:
7 + 5x = -3x + -9x + 3x2

Combine like terms: -3x + -9x = -12x
7 + 5x = -12x + 3x2

Solving
7 + 5x = -12x + 3x2

Solving for variable 'x'.

Combine like terms: 5x + 12x = 17x
7 + 17x + -3x2 = -12x + 3x2 + 12x + -3x2

Reorder the terms:
7 + 17x + -3x2 = -12x + 12x + 3x2 + -3x2

Combine like terms: -12x + 12x = 0
7 + 17x + -3x2 = 0 + 3x2 + -3x2
7 + 17x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
7 + 17x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-2.333333333 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -5.666666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -5.666666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -5.666666667x + x2 = 0 + 2.333333333
-5.666666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-5.666666667x + x2 = 2.333333333

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = 2.333333333 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = 2.333333333 + 8.027777782

Combine like terms: 2.333333333 + 8.027777782 = 10.361111115
8.027777782 + -5.666666667x + x2 = 10.361111115

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 10.361111115

Calculate the square root of the right side: 3.218867987

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 3.218867987 and -3.218867987.

Subproblem 1

x + -2.833333334 = 3.218867987 Simplifying x + -2.833333334 = 3.218867987 Reorder the terms: -2.833333334 + x = 3.218867987 Solving -2.833333334 + x = 3.218867987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 3.218867987 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 3.218867987 + 2.833333334 x = 3.218867987 + 2.833333334 Combine like terms: 3.218867987 + 2.833333334 = 6.052201321 x = 6.052201321 Simplifying x = 6.052201321

Subproblem 2

x + -2.833333334 = -3.218867987 Simplifying x + -2.833333334 = -3.218867987 Reorder the terms: -2.833333334 + x = -3.218867987 Solving -2.833333334 + x = -3.218867987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -3.218867987 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -3.218867987 + 2.833333334 x = -3.218867987 + 2.833333334 Combine like terms: -3.218867987 + 2.833333334 = -0.385534653 x = -0.385534653 Simplifying x = -0.385534653

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.052201321, -0.385534653}

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