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

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


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

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

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

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

Combine like terms: 7x + 2x = 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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