(7x+20)(4x+40)=0

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Solution for (7x+20)(4x+40)=0 equation:


Simplifying
(7x + 20)(4x + 40) = 0

Reorder the terms:
(20 + 7x)(4x + 40) = 0

Reorder the terms:
(20 + 7x)(40 + 4x) = 0

Multiply (20 + 7x) * (40 + 4x)
(20(40 + 4x) + 7x * (40 + 4x)) = 0
((40 * 20 + 4x * 20) + 7x * (40 + 4x)) = 0
((800 + 80x) + 7x * (40 + 4x)) = 0
(800 + 80x + (40 * 7x + 4x * 7x)) = 0
(800 + 80x + (280x + 28x2)) = 0

Combine like terms: 80x + 280x = 360x
(800 + 360x + 28x2) = 0

Solving
800 + 360x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(200 + 90x + 7x2) = 0

Factor a trinomial.
4((10 + x)(20 + 7x)) = 0

Ignore the factor 4.

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

Simplifying
10 + x = 0

Solving
10 + x = 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 + x = 0 + -10

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

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

Simplifying
x = -10

Subproblem 2
Set the factor '(20 + 7x)' equal to zero and attempt to solve:

Simplifying
20 + 7x = 0

Solving
20 + 7x = 0

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

Add '-20' to each side of the equation.
20 + -20 + 7x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 7x = 0 + -20
7x = 0 + -20

Combine like terms: 0 + -20 = -20
7x = -20

Divide each side by '7'.
x = -2.857142857

Simplifying
x = -2.857142857
Solution
x = {-10, -2.857142857}

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