(7x+4)(-3x-2)=0

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Solution for (7x+4)(-3x-2)=0 equation: 


Simplifying
(7x + 4)(-3x + -2) = 0

Reorder the terms:
(4 + 7x)(-3x + -2) = 0

Reorder the terms:
(4 + 7x)(-2 + -3x) = 0

Multiply (4 + 7x) * (-2 + -3x)
(4(-2 + -3x) + 7x * (-2 + -3x)) = 0
((-2 * 4 + -3x * 4) + 7x * (-2 + -3x)) = 0
((-8 + -12x) + 7x * (-2 + -3x)) = 0
(-8 + -12x + (-2 * 7x + -3x * 7x)) = 0
(-8 + -12x + (-14x + -21x2)) = 0

Combine like terms: -12x + -14x = -26x
(-8 + -26x + -21x2) = 0

Solving
-8 + -26x + -21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 26x + 21x2) = 0

Factor a trinomial.
-1((2 + 3x)(4 + 7x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
Set the factor '(4 + 7x)' equal to zero and attempt to solve:

Simplifying
4 + 7x = 0

Solving
4 + 7x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7x = 0 + -4
7x = 0 + -4

Combine like terms: 0 + -4 = -4
7x = -4

Divide each side by '7'.
x = -0.5714285714

Simplifying
x = -0.5714285714
Solution
x = {-0.6666666667, -0.5714285714}

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