(2x+10)(-3x-21)=0

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Solution for (2x+10)(-3x-21)=0 equation: 


Simplifying
(2x + 10)(-3x + -21) = 0

Reorder the terms:
(10 + 2x)(-3x + -21) = 0

Reorder the terms:
(10 + 2x)(-21 + -3x) = 0

Multiply (10 + 2x) * (-21 + -3x)
(10(-21 + -3x) + 2x * (-21 + -3x)) = 0
((-21 * 10 + -3x * 10) + 2x * (-21 + -3x)) = 0
((-210 + -30x) + 2x * (-21 + -3x)) = 0
(-210 + -30x + (-21 * 2x + -3x * 2x)) = 0
(-210 + -30x + (-42x + -6x2)) = 0

Combine like terms: -30x + -42x = -72x
(-210 + -72x + -6x2) = 0

Solving
-210 + -72x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-6'.
-6(35 + 12x + x2) = 0

Factor a trinomial.
-6((7 + x)(5 + x)) = 0

Ignore the factor -6.

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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-7, -5}

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