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

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


Simplifying
5x + 8 = 5x(x + 3)

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

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

Solving
8 + 5x = 15x + 5x2

Solving for variable 'x'.

Combine like terms: 5x + -15x = -10x
8 + -10x + -5x2 = 15x + 5x2 + -15x + -5x2

Reorder the terms:
8 + -10x + -5x2 = 15x + -15x + 5x2 + -5x2

Combine like terms: 15x + -15x = 0
8 + -10x + -5x2 = 0 + 5x2 + -5x2
8 + -10x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
8 + -10x + -5x2 = 0

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

Divide each side by '-5'.
-1.6 + 2x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 2x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 2x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 2x + x2 = 0 + 1.6
2x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
2x + x2 = 1.6

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 1.6 + 1

Reorder the terms:
1 + 2x + x2 = 1.6 + 1

Combine like terms: 1.6 + 1 = 2.6
1 + 2x + x2 = 2.6

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.6

Calculate the square root of the right side: 1.61245155

Break this problem into two subproblems by setting 
(x + 1) equal to 1.61245155 and -1.61245155.

Subproblem 1

x + 1 = 1.61245155 Simplifying x + 1 = 1.61245155 Reorder the terms: 1 + x = 1.61245155 Solving 1 + x = 1.61245155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.61245155 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.61245155 + -1 x = 1.61245155 + -1 Combine like terms: 1.61245155 + -1 = 0.61245155 x = 0.61245155 Simplifying x = 0.61245155

Subproblem 2

x + 1 = -1.61245155 Simplifying x + 1 = -1.61245155 Reorder the terms: 1 + x = -1.61245155 Solving 1 + x = -1.61245155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.61245155 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.61245155 + -1 x = -1.61245155 + -1 Combine like terms: -1.61245155 + -1 = -2.61245155 x = -2.61245155 Simplifying x = -2.61245155

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.61245155, -2.61245155}

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