16(x^2+2x)-36+32x=46x+3(x^2+6)

Solution for 16(x^2+2x)-36+32x=46x+3(x^2+6) equation:

Simplifying
16(x2 + 2x) + -36 + 32x = 46x + 3(x2 + 6)

Reorder the terms:
16(2x + x2) + -36 + 32x = 46x + 3(x2 + 6)
(2x * 16 + x2 * 16) + -36 + 32x = 46x + 3(x2 + 6)
(32x + 16x2) + -36 + 32x = 46x + 3(x2 + 6)

Reorder the terms:
-36 + 32x + 32x + 16x2 = 46x + 3(x2 + 6)

Combine like terms: 32x + 32x = 64x
-36 + 64x + 16x2 = 46x + 3(x2 + 6)

Reorder the terms:
-36 + 64x + 16x2 = 46x + 3(6 + x2)
-36 + 64x + 16x2 = 46x + (6 * 3 + x2 * 3)
-36 + 64x + 16x2 = 46x + (18 + 3x2)

Reorder the terms:
-36 + 64x + 16x2 = 18 + 46x + 3x2

Solving
-36 + 64x + 16x2 = 18 + 46x + 3x2

Solving for variable 'x'.

Reorder the terms:
-36 + -18 + 64x + -46x + 16x2 + -3x2 = 18 + 46x + 3x2 + -18 + -46x + -3x2

Combine like terms: -36 + -18 = -54
-54 + 64x + -46x + 16x2 + -3x2 = 18 + 46x + 3x2 + -18 + -46x + -3x2

Combine like terms: 64x + -46x = 18x
-54 + 18x + 16x2 + -3x2 = 18 + 46x + 3x2 + -18 + -46x + -3x2

Combine like terms: 16x2 + -3x2 = 13x2
-54 + 18x + 13x2 = 18 + 46x + 3x2 + -18 + -46x + -3x2

Reorder the terms:
-54 + 18x + 13x2 = 18 + -18 + 46x + -46x + 3x2 + -3x2

Combine like terms: 18 + -18 = 0
-54 + 18x + 13x2 = 0 + 46x + -46x + 3x2 + -3x2
-54 + 18x + 13x2 = 46x + -46x + 3x2 + -3x2

Combine like terms: 46x + -46x = 0
-54 + 18x + 13x2 = 0 + 3x2 + -3x2
-54 + 18x + 13x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-54 + 18x + 13x2 = 0

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

Divide each side by '13'.
-4.153846154 + 1.384615385x + x2 = 0

Move the constant term to the right:

Add '4.153846154' to each side of the equation.
-4.153846154 + 1.384615385x + 4.153846154 + x2 = 0 + 4.153846154

Reorder the terms:
-4.153846154 + 4.153846154 + 1.384615385x + x2 = 0 + 4.153846154

Combine like terms: -4.153846154 + 4.153846154 = 0.000000000
0.000000000 + 1.384615385x + x2 = 0 + 4.153846154
1.384615385x + x2 = 0 + 4.153846154

Combine like terms: 0 + 4.153846154 = 4.153846154
1.384615385x + x2 = 4.153846154

The x term is 1.384615385x.  Take half its coefficient (0.6923076925).
Square it (0.4792899411) and add it to both sides.

Add '0.4792899411' to each side of the equation.
1.384615385x + 0.4792899411 + x2 = 4.153846154 + 0.4792899411

Reorder the terms:
0.4792899411 + 1.384615385x + x2 = 4.153846154 + 0.4792899411

Combine like terms: 4.153846154 + 0.4792899411 = 4.6331360951
0.4792899411 + 1.384615385x + x2 = 4.6331360951

Factor a perfect square on the left side:
(x + 0.6923076925)(x + 0.6923076925) = 4.6331360951

Calculate the square root of the right side: 2.152472089

Break this problem into two subproblems by setting 
(x + 0.6923076925) equal to 2.152472089 and -2.152472089.

Subproblem 1
x + 0.6923076925 = 2.152472089

Simplifying
x + 0.6923076925 = 2.152472089

Reorder the terms:
0.6923076925 + x = 2.152472089

Solving
0.6923076925 + x = 2.152472089

Solving for variable 'x'.

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

Add '-0.6923076925' to each side of the equation.
0.6923076925 + -0.6923076925 + x = 2.152472089 + -0.6923076925

Combine like terms: 0.6923076925 + -0.6923076925 = 0.0000000000
0.0000000000 + x = 2.152472089 + -0.6923076925
x = 2.152472089 + -0.6923076925

Combine like terms: 2.152472089 + -0.6923076925 = 1.4601643965
x = 1.4601643965

Simplifying
x = 1.4601643965

Subproblem 2
x + 0.6923076925 = -2.152472089

Simplifying
x + 0.6923076925 = -2.152472089

Reorder the terms:
0.6923076925 + x = -2.152472089

Solving
0.6923076925 + x = -2.152472089

Solving for variable 'x'.

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

Add '-0.6923076925' to each side of the equation.
0.6923076925 + -0.6923076925 + x = -2.152472089 + -0.6923076925

Combine like terms: 0.6923076925 + -0.6923076925 = 0.0000000000
0.0000000000 + x = -2.152472089 + -0.6923076925
x = -2.152472089 + -0.6923076925

Combine like terms: -2.152472089 + -0.6923076925 = -2.8447797815
x = -2.8447797815

Simplifying
x = -2.8447797815

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4601643965, -2.8447797815}