(3*x+2)*(2*x+9)-(x+2)*(6*x+1)=(x+1)-(x-6)

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Solution for (3*x+2)*(2*x+9)-(x+2)*(6*x+1)=(x+1)-(x-6) equation: 


Simplifying
(3x + 2)(2x + 9) + -1(x + 2)(6x + 1) = (x + 1) + -1(x + -6)

Reorder the terms:
(2 + 3x)(2x + 9) + -1(x + 2)(6x + 1) = (x + 1) + -1(x + -6)

Reorder the terms:
(2 + 3x)(9 + 2x) + -1(x + 2)(6x + 1) = (x + 1) + -1(x + -6)

Multiply (2 + 3x) * (9 + 2x)
(2(9 + 2x) + 3x * (9 + 2x)) + -1(x + 2)(6x + 1) = (x + 1) + -1(x + -6)
((9 * 2 + 2x * 2) + 3x * (9 + 2x)) + -1(x + 2)(6x + 1) = (x + 1) + -1(x + -6)
((18 + 4x) + 3x * (9 + 2x)) + -1(x + 2)(6x + 1) = (x + 1) + -1(x + -6)
(18 + 4x + (9 * 3x + 2x * 3x)) + -1(x + 2)(6x + 1) = (x + 1) + -1(x + -6)
(18 + 4x + (27x + 6x2)) + -1(x + 2)(6x + 1) = (x + 1) + -1(x + -6)

Combine like terms: 4x + 27x = 31x
(18 + 31x + 6x2) + -1(x + 2)(6x + 1) = (x + 1) + -1(x + -6)

Reorder the terms:
18 + 31x + 6x2 + -1(2 + x)(6x + 1) = (x + 1) + -1(x + -6)

Reorder the terms:
18 + 31x + 6x2 + -1(2 + x)(1 + 6x) = (x + 1) + -1(x + -6)

Multiply (2 + x) * (1 + 6x)
18 + 31x + 6x2 + -1(2(1 + 6x) + x(1 + 6x)) = (x + 1) + -1(x + -6)
18 + 31x + 6x2 + -1((1 * 2 + 6x * 2) + x(1 + 6x)) = (x + 1) + -1(x + -6)
18 + 31x + 6x2 + -1((2 + 12x) + x(1 + 6x)) = (x + 1) + -1(x + -6)
18 + 31x + 6x2 + -1(2 + 12x + (1 * x + 6x * x)) = (x + 1) + -1(x + -6)
18 + 31x + 6x2 + -1(2 + 12x + (1x + 6x2)) = (x + 1) + -1(x + -6)

Combine like terms: 12x + 1x = 13x
18 + 31x + 6x2 + -1(2 + 13x + 6x2) = (x + 1) + -1(x + -6)
18 + 31x + 6x2 + (2 * -1 + 13x * -1 + 6x2 * -1) = (x + 1) + -1(x + -6)
18 + 31x + 6x2 + (-2 + -13x + -6x2) = (x + 1) + -1(x + -6)

Reorder the terms:
18 + -2 + 31x + -13x + 6x2 + -6x2 = (x + 1) + -1(x + -6)

Combine like terms: 18 + -2 = 16
16 + 31x + -13x + 6x2 + -6x2 = (x + 1) + -1(x + -6)

Combine like terms: 31x + -13x = 18x
16 + 18x + 6x2 + -6x2 = (x + 1) + -1(x + -6)

Combine like terms: 6x2 + -6x2 = 0
16 + 18x + 0 = (x + 1) + -1(x + -6)
16 + 18x = (x + 1) + -1(x + -6)

Reorder the terms:
16 + 18x = (1 + x) + -1(x + -6)

Remove parenthesis around (1 + x)
16 + 18x = 1 + x + -1(x + -6)

Reorder the terms:
16 + 18x = 1 + x + -1(-6 + x)
16 + 18x = 1 + x + (-6 * -1 + x * -1)
16 + 18x = 1 + x + (6 + -1x)

Reorder the terms:
16 + 18x = 1 + 6 + x + -1x

Combine like terms: 1 + 6 = 7
16 + 18x = 7 + x + -1x

Combine like terms: x + -1x = 0
16 + 18x = 7 + 0
16 + 18x = 7

Solving
16 + 18x = 7

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + 18x = 7 + -16

Combine like terms: 16 + -16 = 0
0 + 18x = 7 + -16
18x = 7 + -16

Combine like terms: 7 + -16 = -9
18x = -9

Divide each side by '18'.
x = -0.5

Simplifying
x = -0.5

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