3-(x+6)(3x-10)=2(3x+10)-(4x+8x+22)

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Solution for 3-(x+6)(3x-10)=2(3x+10)-(4x+8x+22) equation: 


Simplifying
3 + -1(x + 6)(3x + -10) = 2(3x + 10) + -1(4x + 8x + 22)

Reorder the terms:
3 + -1(6 + x)(3x + -10) = 2(3x + 10) + -1(4x + 8x + 22)

Reorder the terms:
3 + -1(6 + x)(-10 + 3x) = 2(3x + 10) + -1(4x + 8x + 22)

Multiply (6 + x) * (-10 + 3x)
3 + -1(6(-10 + 3x) + x(-10 + 3x)) = 2(3x + 10) + -1(4x + 8x + 22)
3 + -1((-10 * 6 + 3x * 6) + x(-10 + 3x)) = 2(3x + 10) + -1(4x + 8x + 22)
3 + -1((-60 + 18x) + x(-10 + 3x)) = 2(3x + 10) + -1(4x + 8x + 22)
3 + -1(-60 + 18x + (-10 * x + 3x * x)) = 2(3x + 10) + -1(4x + 8x + 22)
3 + -1(-60 + 18x + (-10x + 3x2)) = 2(3x + 10) + -1(4x + 8x + 22)

Combine like terms: 18x + -10x = 8x
3 + -1(-60 + 8x + 3x2) = 2(3x + 10) + -1(4x + 8x + 22)
3 + (-60 * -1 + 8x * -1 + 3x2 * -1) = 2(3x + 10) + -1(4x + 8x + 22)
3 + (60 + -8x + -3x2) = 2(3x + 10) + -1(4x + 8x + 22)

Combine like terms: 3 + 60 = 63
63 + -8x + -3x2 = 2(3x + 10) + -1(4x + 8x + 22)

Reorder the terms:
63 + -8x + -3x2 = 2(10 + 3x) + -1(4x + 8x + 22)
63 + -8x + -3x2 = (10 * 2 + 3x * 2) + -1(4x + 8x + 22)
63 + -8x + -3x2 = (20 + 6x) + -1(4x + 8x + 22)

Reorder the terms:
63 + -8x + -3x2 = 20 + 6x + -1(22 + 4x + 8x)

Combine like terms: 4x + 8x = 12x
63 + -8x + -3x2 = 20 + 6x + -1(22 + 12x)
63 + -8x + -3x2 = 20 + 6x + (22 * -1 + 12x * -1)
63 + -8x + -3x2 = 20 + 6x + (-22 + -12x)

Reorder the terms:
63 + -8x + -3x2 = 20 + -22 + 6x + -12x

Combine like terms: 20 + -22 = -2
63 + -8x + -3x2 = -2 + 6x + -12x

Combine like terms: 6x + -12x = -6x
63 + -8x + -3x2 = -2 + -6x

Solving
63 + -8x + -3x2 = -2 + -6x

Solving for variable 'x'.

Reorder the terms:
63 + 2 + -8x + 6x + -3x2 = -2 + -6x + 2 + 6x

Combine like terms: 63 + 2 = 65
65 + -8x + 6x + -3x2 = -2 + -6x + 2 + 6x

Combine like terms: -8x + 6x = -2x
65 + -2x + -3x2 = -2 + -6x + 2 + 6x

Reorder the terms:
65 + -2x + -3x2 = -2 + 2 + -6x + 6x

Combine like terms: -2 + 2 = 0
65 + -2x + -3x2 = 0 + -6x + 6x
65 + -2x + -3x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
65 + -2x + -3x2 = 0

Factor a trinomial.
(13 + -3x)(5 + x) = 0


Subproblem 1
Set the factor '(13 + -3x)' equal to zero and attempt to solve:

Simplifying
13 + -3x = 0

Solving
13 + -3x = 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 + -3x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -3x = 0 + -13
-3x = 0 + -13

Combine like terms: 0 + -13 = -13
-3x = -13

Divide each side by '-3'.
x = 4.333333333

Simplifying
x = 4.333333333

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {4.333333333, -5}

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