(x+10)(x+5)+(x+-3)(x+12)+(x+11)(x+30)=106

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Solution for (x+10)(x+5)+(x+-3)(x+12)+(x+11)(x+30)=106 equation: 


Simplifying
(x + 10)(x + 5) + (x + -3)(x + 12) + (x + 11)(x + 30) = 106

Reorder the terms:
(10 + x)(x + 5) + (x + -3)(x + 12) + (x + 11)(x + 30) = 106

Reorder the terms:
(10 + x)(5 + x) + (x + -3)(x + 12) + (x + 11)(x + 30) = 106

Multiply (10 + x) * (5 + x)
(10(5 + x) + x(5 + x)) + (x + -3)(x + 12) + (x + 11)(x + 30) = 106
((5 * 10 + x * 10) + x(5 + x)) + (x + -3)(x + 12) + (x + 11)(x + 30) = 106
((50 + 10x) + x(5 + x)) + (x + -3)(x + 12) + (x + 11)(x + 30) = 106
(50 + 10x + (5 * x + x * x)) + (x + -3)(x + 12) + (x + 11)(x + 30) = 106
(50 + 10x + (5x + x2)) + (x + -3)(x + 12) + (x + 11)(x + 30) = 106

Combine like terms: 10x + 5x = 15x
(50 + 15x + x2) + (x + -3)(x + 12) + (x + 11)(x + 30) = 106

Reorder the terms:
50 + 15x + x2 + (-3 + x)(x + 12) + (x + 11)(x + 30) = 106

Reorder the terms:
50 + 15x + x2 + (-3 + x)(12 + x) + (x + 11)(x + 30) = 106

Multiply (-3 + x) * (12 + x)
50 + 15x + x2 + (-3(12 + x) + x(12 + x)) + (x + 11)(x + 30) = 106
50 + 15x + x2 + ((12 * -3 + x * -3) + x(12 + x)) + (x + 11)(x + 30) = 106
50 + 15x + x2 + ((-36 + -3x) + x(12 + x)) + (x + 11)(x + 30) = 106
50 + 15x + x2 + (-36 + -3x + (12 * x + x * x)) + (x + 11)(x + 30) = 106
50 + 15x + x2 + (-36 + -3x + (12x + x2)) + (x + 11)(x + 30) = 106

Combine like terms: -3x + 12x = 9x
50 + 15x + x2 + (-36 + 9x + x2) + (x + 11)(x + 30) = 106

Reorder the terms:
50 + 15x + x2 + -36 + 9x + x2 + (11 + x)(x + 30) = 106

Reorder the terms:
50 + 15x + x2 + -36 + 9x + x2 + (11 + x)(30 + x) = 106

Multiply (11 + x) * (30 + x)
50 + 15x + x2 + -36 + 9x + x2 + (11(30 + x) + x(30 + x)) = 106
50 + 15x + x2 + -36 + 9x + x2 + ((30 * 11 + x * 11) + x(30 + x)) = 106
50 + 15x + x2 + -36 + 9x + x2 + ((330 + 11x) + x(30 + x)) = 106
50 + 15x + x2 + -36 + 9x + x2 + (330 + 11x + (30 * x + x * x)) = 106
50 + 15x + x2 + -36 + 9x + x2 + (330 + 11x + (30x + x2)) = 106

Combine like terms: 11x + 30x = 41x
50 + 15x + x2 + -36 + 9x + x2 + (330 + 41x + x2) = 106

Reorder the terms:
50 + -36 + 330 + 15x + 9x + 41x + x2 + x2 + x2 = 106

Combine like terms: 50 + -36 = 14
14 + 330 + 15x + 9x + 41x + x2 + x2 + x2 = 106

Combine like terms: 14 + 330 = 344
344 + 15x + 9x + 41x + x2 + x2 + x2 = 106

Combine like terms: 15x + 9x = 24x
344 + 24x + 41x + x2 + x2 + x2 = 106

Combine like terms: 24x + 41x = 65x
344 + 65x + x2 + x2 + x2 = 106

Combine like terms: x2 + x2 = 2x2
344 + 65x + 2x2 + x2 = 106

Combine like terms: 2x2 + x2 = 3x2
344 + 65x + 3x2 = 106

Solving
344 + 65x + 3x2 = 106

Solving for variable 'x'.

Reorder the terms:
344 + -106 + 65x + 3x2 = 106 + -106

Combine like terms: 344 + -106 = 238
238 + 65x + 3x2 = 106 + -106

Combine like terms: 106 + -106 = 0
238 + 65x + 3x2 = 0

Factor a trinomial.
(17 + x)(14 + 3x) = 0


Subproblem 1
Set the factor '(17 + x)' equal to zero and attempt to solve:

Simplifying
17 + x = 0

Solving
17 + x = 0

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

Add '-17' to each side of the equation.
17 + -17 + x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + x = 0 + -17
x = 0 + -17

Combine like terms: 0 + -17 = -17
x = -17

Simplifying
x = -17

Subproblem 2
Set the factor '(14 + 3x)' equal to zero and attempt to solve:

Simplifying
14 + 3x = 0

Solving
14 + 3x = 0

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

Add '-14' to each side of the equation.
14 + -14 + 3x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 3x = 0 + -14
3x = 0 + -14

Combine like terms: 0 + -14 = -14
3x = -14

Divide each side by '3'.
x = -4.666666667

Simplifying
x = -4.666666667
Solution
x = {-17, -4.666666667}

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