3x(6x+3)=4(2x-7)3(3x+2)

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Solution for 3x(6x+3)=4(2x-7)3(3x+2) equation:


Simplifying
3x(6x + 3) = 4(2x + -7) * 3(3x + 2)

Reorder the terms:
3x(3 + 6x) = 4(2x + -7) * 3(3x + 2)
(3 * 3x + 6x * 3x) = 4(2x + -7) * 3(3x + 2)
(9x + 18x2) = 4(2x + -7) * 3(3x + 2)

Reorder the terms:
9x + 18x2 = 4(-7 + 2x) * 3(3x + 2)

Reorder the terms:
9x + 18x2 = 4(-7 + 2x) * 3(2 + 3x)

Reorder the terms for easier multiplication:
9x + 18x2 = 4 * 3(-7 + 2x)(2 + 3x)

Multiply 4 * 3
9x + 18x2 = 12(-7 + 2x)(2 + 3x)

Multiply (-7 + 2x) * (2 + 3x)
9x + 18x2 = 12(-7(2 + 3x) + 2x * (2 + 3x))
9x + 18x2 = 12((2 * -7 + 3x * -7) + 2x * (2 + 3x))
9x + 18x2 = 12((-14 + -21x) + 2x * (2 + 3x))
9x + 18x2 = 12(-14 + -21x + (2 * 2x + 3x * 2x))
9x + 18x2 = 12(-14 + -21x + (4x + 6x2))

Combine like terms: -21x + 4x = -17x
9x + 18x2 = 12(-14 + -17x + 6x2)
9x + 18x2 = (-14 * 12 + -17x * 12 + 6x2 * 12)
9x + 18x2 = (-168 + -204x + 72x2)

Solving
9x + 18x2 = -168 + -204x + 72x2

Solving for variable 'x'.

Reorder the terms:
168 + 9x + 204x + 18x2 + -72x2 = -168 + -204x + 72x2 + 168 + 204x + -72x2

Combine like terms: 9x + 204x = 213x
168 + 213x + 18x2 + -72x2 = -168 + -204x + 72x2 + 168 + 204x + -72x2

Combine like terms: 18x2 + -72x2 = -54x2
168 + 213x + -54x2 = -168 + -204x + 72x2 + 168 + 204x + -72x2

Reorder the terms:
168 + 213x + -54x2 = -168 + 168 + -204x + 204x + 72x2 + -72x2

Combine like terms: -168 + 168 = 0
168 + 213x + -54x2 = 0 + -204x + 204x + 72x2 + -72x2
168 + 213x + -54x2 = -204x + 204x + 72x2 + -72x2

Combine like terms: -204x + 204x = 0
168 + 213x + -54x2 = 0 + 72x2 + -72x2
168 + 213x + -54x2 = 72x2 + -72x2

Combine like terms: 72x2 + -72x2 = 0
168 + 213x + -54x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(56 + 71x + -18x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(56 + 71x + -18x2)' equal to zero and attempt to solve:

Simplifying
56 + 71x + -18x2 = 0

Solving
56 + 71x + -18x2 = 0

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
-3.111111111 + -3.944444444x + x2 = 0

Move the constant term to the right:

Add '3.111111111' to each side of the equation.
-3.111111111 + -3.944444444x + 3.111111111 + x2 = 0 + 3.111111111

Reorder the terms:
-3.111111111 + 3.111111111 + -3.944444444x + x2 = 0 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + -3.944444444x + x2 = 0 + 3.111111111
-3.944444444x + x2 = 0 + 3.111111111

Combine like terms: 0 + 3.111111111 = 3.111111111
-3.944444444x + x2 = 3.111111111

The x term is -3.944444444x.  Take half its coefficient (-1.972222222).
Square it (3.889660493) and add it to both sides.

Add '3.889660493' to each side of the equation.
-3.944444444x + 3.889660493 + x2 = 3.111111111 + 3.889660493

Reorder the terms:
3.889660493 + -3.944444444x + x2 = 3.111111111 + 3.889660493

Combine like terms: 3.111111111 + 3.889660493 = 7.000771604
3.889660493 + -3.944444444x + x2 = 7.000771604

Factor a perfect square on the left side:
(x + -1.972222222)(x + -1.972222222) = 7.000771604

Calculate the square root of the right side: 2.645897126

Break this problem into two subproblems by setting 
(x + -1.972222222) equal to 2.645897126 and -2.645897126.


Subproblem 1
x + -1.972222222 = 2.645897126

Simplifying
x + -1.972222222 = 2.645897126

Reorder the terms:
-1.972222222 + x = 2.645897126

Solving
-1.972222222 + x = 2.645897126

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.972222222' to each side of the equation.
-1.972222222 + 1.972222222 + x = 2.645897126 + 1.972222222

Combine like terms: -1.972222222 + 1.972222222 = 0.000000000
0.000000000 + x = 2.645897126 + 1.972222222
x = 2.645897126 + 1.972222222

Combine like terms: 2.645897126 + 1.972222222 = 4.618119348
x = 4.618119348

Simplifying
x = 4.618119348


Subproblem 2
x + -1.972222222 = -2.645897126

Simplifying
x + -1.972222222 = -2.645897126

Reorder the terms:
-1.972222222 + x = -2.645897126

Solving
-1.972222222 + x = -2.645897126

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.972222222' to each side of the equation.
-1.972222222 + 1.972222222 + x = -2.645897126 + 1.972222222

Combine like terms: -1.972222222 + 1.972222222 = 0.000000000
0.000000000 + x = -2.645897126 + 1.972222222
x = -2.645897126 + 1.972222222

Combine like terms: -2.645897126 + 1.972222222 = -0.673674904
x = -0.673674904

Simplifying
x = -0.673674904


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.618119348, -0.673674904}
Solution
x = {4.618119348, -0.673674904}

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