6(x+3)+7-x=4x(x+3)

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Solution for 6(x+3)+7-x=4x(x+3) equation:


Simplifying
6(x + 3) + 7 + -1x = 4x(x + 3)

Reorder the terms:
6(3 + x) + 7 + -1x = 4x(x + 3)
(3 * 6 + x * 6) + 7 + -1x = 4x(x + 3)
(18 + 6x) + 7 + -1x = 4x(x + 3)

Reorder the terms:
18 + 7 + 6x + -1x = 4x(x + 3)

Combine like terms: 18 + 7 = 25
25 + 6x + -1x = 4x(x + 3)

Combine like terms: 6x + -1x = 5x
25 + 5x = 4x(x + 3)

Reorder the terms:
25 + 5x = 4x(3 + x)
25 + 5x = (3 * 4x + x * 4x)
25 + 5x = (12x + 4x2)

Solving
25 + 5x = 12x + 4x2

Solving for variable 'x'.

Combine like terms: 5x + -12x = -7x
25 + -7x + -4x2 = 12x + 4x2 + -12x + -4x2

Reorder the terms:
25 + -7x + -4x2 = 12x + -12x + 4x2 + -4x2

Combine like terms: 12x + -12x = 0
25 + -7x + -4x2 = 0 + 4x2 + -4x2
25 + -7x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
25 + -7x + -4x2 = 0

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

Divide each side by '-4'.
-6.25 + 1.75x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 1.75x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 1.75x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 1.75x + x2 = 0 + 6.25
1.75x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
1.75x + x2 = 6.25

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 = 6.25 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 6.25 + 0.765625

Combine like terms: 6.25 + 0.765625 = 7.015625
0.765625 + 1.75x + x2 = 7.015625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 7.015625

Calculate the square root of the right side: 2.648702513

Break this problem into two subproblems by setting 
(x + 0.875) equal to 2.648702513 and -2.648702513.

Subproblem 1

x + 0.875 = 2.648702513 Simplifying x + 0.875 = 2.648702513 Reorder the terms: 0.875 + x = 2.648702513 Solving 0.875 + x = 2.648702513 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 = 2.648702513 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.648702513 + -0.875 x = 2.648702513 + -0.875 Combine like terms: 2.648702513 + -0.875 = 1.773702513 x = 1.773702513 Simplifying x = 1.773702513

Subproblem 2

x + 0.875 = -2.648702513 Simplifying x + 0.875 = -2.648702513 Reorder the terms: 0.875 + x = -2.648702513 Solving 0.875 + x = -2.648702513 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 = -2.648702513 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.648702513 + -0.875 x = -2.648702513 + -0.875 Combine like terms: -2.648702513 + -0.875 = -3.523702513 x = -3.523702513 Simplifying x = -3.523702513

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.773702513, -3.523702513}

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