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

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


Simplifying
3(x + 5) + -2 = 2(2x + 5) * x

Reorder the terms:
3(5 + x) + -2 = 2(2x + 5) * x
(5 * 3 + x * 3) + -2 = 2(2x + 5) * x
(15 + 3x) + -2 = 2(2x + 5) * x

Reorder the terms:
15 + -2 + 3x = 2(2x + 5) * x

Combine like terms: 15 + -2 = 13
13 + 3x = 2(2x + 5) * x

Reorder the terms:
13 + 3x = 2(5 + 2x) * x

Reorder the terms for easier multiplication:
13 + 3x = 2x(5 + 2x)
13 + 3x = (5 * 2x + 2x * 2x)
13 + 3x = (10x + 4x2)

Solving
13 + 3x = 10x + 4x2

Solving for variable 'x'.

Combine like terms: 3x + -10x = -7x
13 + -7x + -4x2 = 10x + 4x2 + -10x + -4x2

Reorder the terms:
13 + -7x + -4x2 = 10x + -10x + 4x2 + -4x2

Combine like terms: 10x + -10x = 0
13 + -7x + -4x2 = 0 + 4x2 + -4x2
13 + -7x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
13 + -7x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-3.25 + 1.75x + x2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + 1.75x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + 1.75x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + 1.75x + x2 = 0 + 3.25
1.75x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
1.75x + x2 = 3.25

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = 3.25 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 3.25 + 0.765625

Combine like terms: 3.25 + 0.765625 = 4.015625
0.765625 + 1.75x + x2 = 4.015625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 4.015625

Calculate the square root of the right side: 2.003902443

Break this problem into two subproblems by setting 
(x + 0.875) equal to 2.003902443 and -2.003902443.

Subproblem 1

x + 0.875 = 2.003902443 Simplifying x + 0.875 = 2.003902443 Reorder the terms: 0.875 + x = 2.003902443 Solving 0.875 + x = 2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 2.003902443 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.003902443 + -0.875 x = 2.003902443 + -0.875 Combine like terms: 2.003902443 + -0.875 = 1.128902443 x = 1.128902443 Simplifying x = 1.128902443

Subproblem 2

x + 0.875 = -2.003902443 Simplifying x + 0.875 = -2.003902443 Reorder the terms: 0.875 + x = -2.003902443 Solving 0.875 + x = -2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -2.003902443 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.003902443 + -0.875 x = -2.003902443 + -0.875 Combine like terms: -2.003902443 + -0.875 = -2.878902443 x = -2.878902443 Simplifying x = -2.878902443

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.128902443, -2.878902443}

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