(3x+14)(x+1)=-10

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Solution for (3x+14)(x+1)=-10 equation: 


Simplifying
(3x + 14)(x + 1) = -10

Reorder the terms:
(14 + 3x)(x + 1) = -10

Reorder the terms:
(14 + 3x)(1 + x) = -10

Multiply (14 + 3x) * (1 + x)
(14(1 + x) + 3x * (1 + x)) = -10
((1 * 14 + x * 14) + 3x * (1 + x)) = -10
((14 + 14x) + 3x * (1 + x)) = -10
(14 + 14x + (1 * 3x + x * 3x)) = -10
(14 + 14x + (3x + 3x2)) = -10

Combine like terms: 14x + 3x = 17x
(14 + 17x + 3x2) = -10

Solving
14 + 17x + 3x2 = -10

Solving for variable 'x'.

Reorder the terms:
14 + 10 + 17x + 3x2 = -10 + 10

Combine like terms: 14 + 10 = 24
24 + 17x + 3x2 = -10 + 10

Combine like terms: -10 + 10 = 0
24 + 17x + 3x2 = 0

Factor a trinomial.
(3 + x)(8 + 3x) = 0


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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3

Subproblem 2
Set the factor '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667
Solution
x = {-3, -2.666666667}

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