(x+7)(2x+1)=0

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Solution for (x+7)(2x+1)=0 equation: 


Simplifying
(x + 7)(2x + 1) = 0

Reorder the terms:
(7 + x)(2x + 1) = 0

Reorder the terms:
(7 + x)(1 + 2x) = 0

Multiply (7 + x) * (1 + 2x)
(7(1 + 2x) + x(1 + 2x)) = 0
((1 * 7 + 2x * 7) + x(1 + 2x)) = 0
((7 + 14x) + x(1 + 2x)) = 0
(7 + 14x + (1 * x + 2x * x)) = 0
(7 + 14x + (1x + 2x2)) = 0

Combine like terms: 14x + 1x = 15x
(7 + 15x + 2x2) = 0

Solving
7 + 15x + 2x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

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 = {-7, -0.5}

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