(2x+7)(x+1)=12

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Solution for (2x+7)(x+1)=12 equation:


Simplifying
(2x + 7)(x + 1) = 12

Reorder the terms:
(7 + 2x)(x + 1) = 12

Reorder the terms:
(7 + 2x)(1 + x) = 12

Multiply (7 + 2x) * (1 + x)
(7(1 + x) + 2x * (1 + x)) = 12
((1 * 7 + x * 7) + 2x * (1 + x)) = 12
((7 + 7x) + 2x * (1 + x)) = 12
(7 + 7x + (1 * 2x + x * 2x)) = 12
(7 + 7x + (2x + 2x2)) = 12

Combine like terms: 7x + 2x = 9x
(7 + 9x + 2x2) = 12

Solving
7 + 9x + 2x2 = 12

Solving for variable 'x'.

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

Combine like terms: 7 + -12 = -5
-5 + 9x + 2x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-5 + 9x + 2x2 = 0

Factor a trinomial.
(-5 + -1x)(1 + -2x) = 0

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {-5, 0.5}

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