3(x+4)-2=2(2x+5)x

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Solution for 3(x+4)-2=2(2x+5)x equation:


Simplifying
3(x + 4) + -2 = 2(2x + 5) * x

Reorder the terms:
3(4 + x) + -2 = 2(2x + 5) * x
(4 * 3 + x * 3) + -2 = 2(2x + 5) * x
(12 + 3x) + -2 = 2(2x + 5) * x

Reorder the terms:
12 + -2 + 3x = 2(2x + 5) * x

Combine like terms: 12 + -2 = 10
10 + 3x = 2(2x + 5) * x

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

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

Solving
10 + 3x = 10x + 4x2

Solving for variable 'x'.

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

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

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

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

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

Divide each side by '-4'.
-2.5 + 1.75x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 1.75x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 1.75x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 1.75x + x2 = 0 + 2.5
1.75x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
1.75x + x2 = 2.5

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 = 2.5 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 2.5 + 0.765625

Combine like terms: 2.5 + 0.765625 = 3.265625
0.765625 + 1.75x + x2 = 3.265625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 3.265625

Calculate the square root of the right side: 1.807104037

Break this problem into two subproblems by setting 
(x + 0.875) equal to 1.807104037 and -1.807104037.

Subproblem 1

x + 0.875 = 1.807104037 Simplifying x + 0.875 = 1.807104037 Reorder the terms: 0.875 + x = 1.807104037 Solving 0.875 + x = 1.807104037 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 = 1.807104037 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.807104037 + -0.875 x = 1.807104037 + -0.875 Combine like terms: 1.807104037 + -0.875 = 0.932104037 x = 0.932104037 Simplifying x = 0.932104037

Subproblem 2

x + 0.875 = -1.807104037 Simplifying x + 0.875 = -1.807104037 Reorder the terms: 0.875 + x = -1.807104037 Solving 0.875 + x = -1.807104037 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 = -1.807104037 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.807104037 + -0.875 x = -1.807104037 + -0.875 Combine like terms: -1.807104037 + -0.875 = -2.682104037 x = -2.682104037 Simplifying x = -2.682104037

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.932104037, -2.682104037}

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