(x+1)(2x+7)=3(x+4)-9

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Solution for (x+1)(2x+7)=3(x+4)-9 equation: 


Simplifying
(x + 1)(2x + 7) = 3(x + 4) + -9

Reorder the terms:
(1 + x)(2x + 7) = 3(x + 4) + -9

Reorder the terms:
(1 + x)(7 + 2x) = 3(x + 4) + -9

Multiply (1 + x) * (7 + 2x)
(1(7 + 2x) + x(7 + 2x)) = 3(x + 4) + -9
((7 * 1 + 2x * 1) + x(7 + 2x)) = 3(x + 4) + -9
((7 + 2x) + x(7 + 2x)) = 3(x + 4) + -9
(7 + 2x + (7 * x + 2x * x)) = 3(x + 4) + -9
(7 + 2x + (7x + 2x2)) = 3(x + 4) + -9

Combine like terms: 2x + 7x = 9x
(7 + 9x + 2x2) = 3(x + 4) + -9

Reorder the terms:
7 + 9x + 2x2 = 3(4 + x) + -9
7 + 9x + 2x2 = (4 * 3 + x * 3) + -9
7 + 9x + 2x2 = (12 + 3x) + -9

Reorder the terms:
7 + 9x + 2x2 = 12 + -9 + 3x

Combine like terms: 12 + -9 = 3
7 + 9x + 2x2 = 3 + 3x

Solving
7 + 9x + 2x2 = 3 + 3x

Solving for variable 'x'.

Reorder the terms:
7 + -3 + 9x + -3x + 2x2 = 3 + 3x + -3 + -3x

Combine like terms: 7 + -3 = 4
4 + 9x + -3x + 2x2 = 3 + 3x + -3 + -3x

Combine like terms: 9x + -3x = 6x
4 + 6x + 2x2 = 3 + 3x + -3 + -3x

Reorder the terms:
4 + 6x + 2x2 = 3 + -3 + 3x + -3x

Combine like terms: 3 + -3 = 0
4 + 6x + 2x2 = 0 + 3x + -3x
4 + 6x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
4 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 3x + x2) = 0

Factor a trinomial.
2((2 + x)(1 + x)) = 0

Ignore the factor 2.

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-2, -1}

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