(4x+14)(5x+20)=0

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Solution for (4x+14)(5x+20)=0 equation: 


Simplifying
(4x + 14)(5x + 20) = 0

Reorder the terms:
(14 + 4x)(5x + 20) = 0

Reorder the terms:
(14 + 4x)(20 + 5x) = 0

Multiply (14 + 4x) * (20 + 5x)
(14(20 + 5x) + 4x * (20 + 5x)) = 0
((20 * 14 + 5x * 14) + 4x * (20 + 5x)) = 0
((280 + 70x) + 4x * (20 + 5x)) = 0
(280 + 70x + (20 * 4x + 5x * 4x)) = 0
(280 + 70x + (80x + 20x2)) = 0

Combine like terms: 70x + 80x = 150x
(280 + 150x + 20x2) = 0

Solving
280 + 150x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(28 + 15x + 2x2) = 0

Factor a trinomial.
10((4 + x)(7 + 2x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4

Subproblem 2
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
Solution
x = {-4, -3.5}

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