(x+9)(2x+1)+(x+6)(8x+2)=4(2x+1)(8x+2)

Solution for (x+9)(2x+1)+(x+6)(8x+2)=4(2x+1)(8x+2) equation:

Simplifying
(x + 9)(2x + 1) + (x + 6)(8x + 2) = 4(2x + 1)(8x + 2)

Reorder the terms:
(9 + x)(2x + 1) + (x + 6)(8x + 2) = 4(2x + 1)(8x + 2)

Reorder the terms:
(9 + x)(1 + 2x) + (x + 6)(8x + 2) = 4(2x + 1)(8x + 2)

Multiply (9 + x) * (1 + 2x)
(9(1 + 2x) + x(1 + 2x)) + (x + 6)(8x + 2) = 4(2x + 1)(8x + 2)
((1 * 9 + 2x * 9) + x(1 + 2x)) + (x + 6)(8x + 2) = 4(2x + 1)(8x + 2)
((9 + 18x) + x(1 + 2x)) + (x + 6)(8x + 2) = 4(2x + 1)(8x + 2)
(9 + 18x + (1 * x + 2x * x)) + (x + 6)(8x + 2) = 4(2x + 1)(8x + 2)
(9 + 18x + (1x + 2x2)) + (x + 6)(8x + 2) = 4(2x + 1)(8x + 2)

Combine like terms: 18x + 1x = 19x
(9 + 19x + 2x2) + (x + 6)(8x + 2) = 4(2x + 1)(8x + 2)

Reorder the terms:
9 + 19x + 2x2 + (6 + x)(8x + 2) = 4(2x + 1)(8x + 2)

Reorder the terms:
9 + 19x + 2x2 + (6 + x)(2 + 8x) = 4(2x + 1)(8x + 2)

Multiply (6 + x) * (2 + 8x)
9 + 19x + 2x2 + (6(2 + 8x) + x(2 + 8x)) = 4(2x + 1)(8x + 2)
9 + 19x + 2x2 + ((2 * 6 + 8x * 6) + x(2 + 8x)) = 4(2x + 1)(8x + 2)
9 + 19x + 2x2 + ((12 + 48x) + x(2 + 8x)) = 4(2x + 1)(8x + 2)
9 + 19x + 2x2 + (12 + 48x + (2 * x + 8x * x)) = 4(2x + 1)(8x + 2)
9 + 19x + 2x2 + (12 + 48x + (2x + 8x2)) = 4(2x + 1)(8x + 2)

Combine like terms: 48x + 2x = 50x
9 + 19x + 2x2 + (12 + 50x + 8x2) = 4(2x + 1)(8x + 2)

Reorder the terms:
9 + 12 + 19x + 50x + 2x2 + 8x2 = 4(2x + 1)(8x + 2)

Combine like terms: 9 + 12 = 21
21 + 19x + 50x + 2x2 + 8x2 = 4(2x + 1)(8x + 2)

Combine like terms: 19x + 50x = 69x
21 + 69x + 2x2 + 8x2 = 4(2x + 1)(8x + 2)

Combine like terms: 2x2 + 8x2 = 10x2
21 + 69x + 10x2 = 4(2x + 1)(8x + 2)

Reorder the terms:
21 + 69x + 10x2 = 4(1 + 2x)(8x + 2)

Reorder the terms:
21 + 69x + 10x2 = 4(1 + 2x)(2 + 8x)

Multiply (1 + 2x) * (2 + 8x)
21 + 69x + 10x2 = 4(1(2 + 8x) + 2x * (2 + 8x))
21 + 69x + 10x2 = 4((2 * 1 + 8x * 1) + 2x * (2 + 8x))
21 + 69x + 10x2 = 4((2 + 8x) + 2x * (2 + 8x))
21 + 69x + 10x2 = 4(2 + 8x + (2 * 2x + 8x * 2x))
21 + 69x + 10x2 = 4(2 + 8x + (4x + 16x2))

Combine like terms: 8x + 4x = 12x
21 + 69x + 10x2 = 4(2 + 12x + 16x2)
21 + 69x + 10x2 = (2 * 4 + 12x * 4 + 16x2 * 4)
21 + 69x + 10x2 = (8 + 48x + 64x2)

Solving
21 + 69x + 10x2 = 8 + 48x + 64x2

Solving for variable 'x'.

Reorder the terms:
21 + -8 + 69x + -48x + 10x2 + -64x2 = 8 + 48x + 64x2 + -8 + -48x + -64x2

Combine like terms: 21 + -8 = 13
13 + 69x + -48x + 10x2 + -64x2 = 8 + 48x + 64x2 + -8 + -48x + -64x2

Combine like terms: 69x + -48x = 21x
13 + 21x + 10x2 + -64x2 = 8 + 48x + 64x2 + -8 + -48x + -64x2

Combine like terms: 10x2 + -64x2 = -54x2
13 + 21x + -54x2 = 8 + 48x + 64x2 + -8 + -48x + -64x2

Reorder the terms:
13 + 21x + -54x2 = 8 + -8 + 48x + -48x + 64x2 + -64x2

Combine like terms: 8 + -8 = 0
13 + 21x + -54x2 = 0 + 48x + -48x + 64x2 + -64x2
13 + 21x + -54x2 = 48x + -48x + 64x2 + -64x2

Combine like terms: 48x + -48x = 0
13 + 21x + -54x2 = 0 + 64x2 + -64x2
13 + 21x + -54x2 = 64x2 + -64x2

Combine like terms: 64x2 + -64x2 = 0
13 + 21x + -54x2 = 0

Factor a trinomial.
(13 + -18x)(1 + 3x) = 0

Subproblem 1
Set the factor '(13 + -18x)' equal to zero and attempt to solve:

Simplifying
13 + -18x = 0

Solving
13 + -18x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -18x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -18x = 0 + -13
-18x = 0 + -13

Combine like terms: 0 + -13 = -13
-18x = -13

Divide each side by '-18'.
x = 0.7222222222

Simplifying
x = 0.7222222222
Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {0.7222222222, -0.3333333333}