(4x+13)(10x+14)=0

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Solution for (4x+13)(10x+14)=0 equation: 


Simplifying
(4x + 13)(10x + 14) = 0

Reorder the terms:
(13 + 4x)(10x + 14) = 0

Reorder the terms:
(13 + 4x)(14 + 10x) = 0

Multiply (13 + 4x) * (14 + 10x)
(13(14 + 10x) + 4x * (14 + 10x)) = 0
((14 * 13 + 10x * 13) + 4x * (14 + 10x)) = 0
((182 + 130x) + 4x * (14 + 10x)) = 0
(182 + 130x + (14 * 4x + 10x * 4x)) = 0
(182 + 130x + (56x + 40x2)) = 0

Combine like terms: 130x + 56x = 186x
(182 + 186x + 40x2) = 0

Solving
182 + 186x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(91 + 93x + 20x2) = 0

Factor a trinomial.
2((13 + 4x)(7 + 5x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(13 + 4x)' equal to zero and attempt to solve:

Simplifying
13 + 4x = 0

Solving
13 + 4x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 4x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 4x = 0 + -13
4x = 0 + -13

Combine like terms: 0 + -13 = -13
4x = -13

Divide each side by '4'.
x = -3.25

Simplifying
x = -3.25

Subproblem 2
Set the factor '(7 + 5x)' equal to zero and attempt to solve:

Simplifying
7 + 5x = 0

Solving
7 + 5x = 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 + 5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5x = 0 + -7
5x = 0 + -7

Combine like terms: 0 + -7 = -7
5x = -7

Divide each side by '5'.
x = -1.4

Simplifying
x = -1.4
Solution
x = {-3.25, -1.4}

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