(7x+11)(10x+5)=0

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Solution for (7x+11)(10x+5)=0 equation: 


Simplifying
(7x + 11)(10x + 5) = 0

Reorder the terms:
(11 + 7x)(10x + 5) = 0

Reorder the terms:
(11 + 7x)(5 + 10x) = 0

Multiply (11 + 7x) * (5 + 10x)
(11(5 + 10x) + 7x * (5 + 10x)) = 0
((5 * 11 + 10x * 11) + 7x * (5 + 10x)) = 0
((55 + 110x) + 7x * (5 + 10x)) = 0
(55 + 110x + (5 * 7x + 10x * 7x)) = 0
(55 + 110x + (35x + 70x2)) = 0

Combine like terms: 110x + 35x = 145x
(55 + 145x + 70x2) = 0

Solving
55 + 145x + 70x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(11 + 29x + 14x2) = 0

Factor a trinomial.
5((11 + 7x)(1 + 2x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(11 + 7x)' equal to zero and attempt to solve:

Simplifying
11 + 7x = 0

Solving
11 + 7x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 7x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 7x = 0 + -11
7x = 0 + -11

Combine like terms: 0 + -11 = -11
7x = -11

Divide each side by '7'.
x = -1.571428571

Simplifying
x = -1.571428571

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-1.571428571, -0.5}

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