(-3x-7)(2x+1)=0

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Solution for (-3x-7)(2x+1)=0 equation: 


Simplifying
(-3x + -7)(2x + 1) = 0

Reorder the terms:
(-7 + -3x)(2x + 1) = 0

Reorder the terms:
(-7 + -3x)(1 + 2x) = 0

Multiply (-7 + -3x) * (1 + 2x)
(-7(1 + 2x) + -3x * (1 + 2x)) = 0
((1 * -7 + 2x * -7) + -3x * (1 + 2x)) = 0
((-7 + -14x) + -3x * (1 + 2x)) = 0
(-7 + -14x + (1 * -3x + 2x * -3x)) = 0
(-7 + -14x + (-3x + -6x2)) = 0

Combine like terms: -14x + -3x = -17x
(-7 + -17x + -6x2) = 0

Solving
-7 + -17x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 17x + 6x2) = 0

Factor a trinomial.
-1((7 + 3x)(1 + 2x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 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 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333

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 = {-2.333333333, -0.5}

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