8x-3=5(x+1)3x-8

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Solution for 8x-3=5(x+1)3x-8 equation: 


Simplifying
8x + -3 = 5(x + 1) * 3x + -8

Reorder the terms:
-3 + 8x = 5(x + 1) * 3x + -8

Reorder the terms:
-3 + 8x = 5(1 + x) * 3x + -8

Reorder the terms for easier multiplication:
-3 + 8x = 5 * 3x(1 + x) + -8

Multiply 5 * 3
-3 + 8x = 15x(1 + x) + -8
-3 + 8x = (1 * 15x + x * 15x) + -8
-3 + 8x = (15x + 15x2) + -8

Reorder the terms:
-3 + 8x = -8 + 15x + 15x2

Solving
-3 + 8x = -8 + 15x + 15x2

Solving for variable 'x'.

Reorder the terms:
-3 + 8 + 8x + -15x + -15x2 = -8 + 15x + 15x2 + 8 + -15x + -15x2

Combine like terms: -3 + 8 = 5
5 + 8x + -15x + -15x2 = -8 + 15x + 15x2 + 8 + -15x + -15x2

Combine like terms: 8x + -15x = -7x
5 + -7x + -15x2 = -8 + 15x + 15x2 + 8 + -15x + -15x2

Reorder the terms:
5 + -7x + -15x2 = -8 + 8 + 15x + -15x + 15x2 + -15x2

Combine like terms: -8 + 8 = 0
5 + -7x + -15x2 = 0 + 15x + -15x + 15x2 + -15x2
5 + -7x + -15x2 = 15x + -15x + 15x2 + -15x2

Combine like terms: 15x + -15x = 0
5 + -7x + -15x2 = 0 + 15x2 + -15x2
5 + -7x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
5 + -7x + -15x2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-0.3333333333 + 0.4666666667x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.4666666667x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.4666666667x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.4666666667x + x2 = 0 + 0.3333333333
0.4666666667x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.4666666667x + x2 = 0.3333333333

The x term is 0.4666666667x.  Take half its coefficient (0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
0.4666666667x + 0.05444444448 + x2 = 0.3333333333 + 0.05444444448

Reorder the terms:
0.05444444448 + 0.4666666667x + x2 = 0.3333333333 + 0.05444444448

Combine like terms: 0.3333333333 + 0.05444444448 = 0.38777777778
0.05444444448 + 0.4666666667x + x2 = 0.38777777778

Factor a perfect square on the left side:
(x + 0.2333333334)(x + 0.2333333334) = 0.38777777778

Calculate the square root of the right side: 0.622718056

Break this problem into two subproblems by setting 
(x + 0.2333333334) equal to 0.622718056 and -0.622718056.


Subproblem 1
x + 0.2333333334 = 0.622718056

Simplifying
x + 0.2333333334 = 0.622718056

Reorder the terms:
0.2333333334 + x = 0.622718056

Solving
0.2333333334 + x = 0.622718056

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2333333334' to each side of the equation.
0.2333333334 + -0.2333333334 + x = 0.622718056 + -0.2333333334

Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000
0.0000000000 + x = 0.622718056 + -0.2333333334
x = 0.622718056 + -0.2333333334

Combine like terms: 0.622718056 + -0.2333333334 = 0.3893847226
x = 0.3893847226

Simplifying
x = 0.3893847226


Subproblem 2
x + 0.2333333334 = -0.622718056

Simplifying
x + 0.2333333334 = -0.622718056

Reorder the terms:
0.2333333334 + x = -0.622718056

Solving
0.2333333334 + x = -0.622718056

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2333333334' to each side of the equation.
0.2333333334 + -0.2333333334 + x = -0.622718056 + -0.2333333334

Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000
0.0000000000 + x = -0.622718056 + -0.2333333334
x = -0.622718056 + -0.2333333334

Combine like terms: -0.622718056 + -0.2333333334 = -0.8560513894
x = -0.8560513894

Simplifying
x = -0.8560513894


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3893847226, -0.8560513894}

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