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

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


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

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

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

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

Combine like terms: 2x + 7x = 9x
0 = (7 + 9x + 2x2)

Solving
0 = 7 + 9x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -7 = -7
-7 + -9x + -2x2 = 7 + 9x + 2x2 + -7 + -9x + -2x2

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

Combine like terms: 7 + -7 = 0
-7 + -9x + -2x2 = 0 + 9x + -9x + 2x2 + -2x2
-7 + -9x + -2x2 = 9x + -9x + 2x2 + -2x2

Combine like terms: 9x + -9x = 0
-7 + -9x + -2x2 = 0 + 2x2 + -2x2
-7 + -9x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-7 + -9x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 9x + 2x2) = 0

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

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

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 = {-3.5, -1}

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