8x-5x(x+3)=(7x-1)3

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Solution for 8x-5x(x+3)=(7x-1)3 equation:


Simplifying
8x + -5x(x + 3) = (7x + -1) * 3

Reorder the terms:
8x + -5x(3 + x) = (7x + -1) * 3
8x + (3 * -5x + x * -5x) = (7x + -1) * 3
8x + (-15x + -5x2) = (7x + -1) * 3

Combine like terms: 8x + -15x = -7x
-7x + -5x2 = (7x + -1) * 3

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

Reorder the terms for easier multiplication:
-7x + -5x2 = 3(-1 + 7x)
-7x + -5x2 = (-1 * 3 + 7x * 3)
-7x + -5x2 = (-3 + 21x)

Solving
-7x + -5x2 = -3 + 21x

Solving for variable 'x'.

Reorder the terms:
3 + -7x + -21x + -5x2 = -3 + 21x + 3 + -21x

Combine like terms: -7x + -21x = -28x
3 + -28x + -5x2 = -3 + 21x + 3 + -21x

Reorder the terms:
3 + -28x + -5x2 = -3 + 3 + 21x + -21x

Combine like terms: -3 + 3 = 0
3 + -28x + -5x2 = 0 + 21x + -21x
3 + -28x + -5x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
3 + -28x + -5x2 = 0

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

Divide each side by '-5'.
-0.6 + 5.6x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 5.6x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 5.6x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 5.6x + x2 = 0 + 0.6
5.6x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
5.6x + x2 = 0.6

The x term is 5.6x.  Take half its coefficient (2.8).
Square it (7.84) and add it to both sides.

Add '7.84' to each side of the equation.
5.6x + 7.84 + x2 = 0.6 + 7.84

Reorder the terms:
7.84 + 5.6x + x2 = 0.6 + 7.84

Combine like terms: 0.6 + 7.84 = 8.44
7.84 + 5.6x + x2 = 8.44

Factor a perfect square on the left side:
(x + 2.8)(x + 2.8) = 8.44

Calculate the square root of the right side: 2.905167809

Break this problem into two subproblems by setting 
(x + 2.8) equal to 2.905167809 and -2.905167809.

Subproblem 1

x + 2.8 = 2.905167809 Simplifying x + 2.8 = 2.905167809 Reorder the terms: 2.8 + x = 2.905167809 Solving 2.8 + x = 2.905167809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = 2.905167809 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = 2.905167809 + -2.8 x = 2.905167809 + -2.8 Combine like terms: 2.905167809 + -2.8 = 0.105167809 x = 0.105167809 Simplifying x = 0.105167809

Subproblem 2

x + 2.8 = -2.905167809 Simplifying x + 2.8 = -2.905167809 Reorder the terms: 2.8 + x = -2.905167809 Solving 2.8 + x = -2.905167809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = -2.905167809 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = -2.905167809 + -2.8 x = -2.905167809 + -2.8 Combine like terms: -2.905167809 + -2.8 = -5.705167809 x = -5.705167809 Simplifying x = -5.705167809

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.105167809, -5.705167809}

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