(-3x-10)(7x+8)=0

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Solution for (-3x-10)(7x+8)=0 equation: 


Simplifying
(-3x + -10)(7x + 8) = 0

Reorder the terms:
(-10 + -3x)(7x + 8) = 0

Reorder the terms:
(-10 + -3x)(8 + 7x) = 0

Multiply (-10 + -3x) * (8 + 7x)
(-10(8 + 7x) + -3x * (8 + 7x)) = 0
((8 * -10 + 7x * -10) + -3x * (8 + 7x)) = 0
((-80 + -70x) + -3x * (8 + 7x)) = 0
(-80 + -70x + (8 * -3x + 7x * -3x)) = 0
(-80 + -70x + (-24x + -21x2)) = 0

Combine like terms: -70x + -24x = -94x
(-80 + -94x + -21x2) = 0

Solving
-80 + -94x + -21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(80 + 94x + 21x2) = 0

Factor a trinomial.
-1((10 + 3x)(8 + 7x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(10 + 3x)' equal to zero and attempt to solve:

Simplifying
10 + 3x = 0

Solving
10 + 3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3x = 0 + -10
3x = 0 + -10

Combine like terms: 0 + -10 = -10
3x = -10

Divide each side by '3'.
x = -3.333333333

Simplifying
x = -3.333333333

Subproblem 2
Set the factor '(8 + 7x)' equal to zero and attempt to solve:

Simplifying
8 + 7x = 0

Solving
8 + 7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7x = 0 + -8
7x = 0 + -8

Combine like terms: 0 + -8 = -8
7x = -8

Divide each side by '7'.
x = -1.142857143

Simplifying
x = -1.142857143
Solution
x = {-3.333333333, -1.142857143}

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