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

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


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

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

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

Multiply (10 + 5x) * (7 + 5x)
(10(7 + 5x) + 5x * (7 + 5x)) = 0
((7 * 10 + 5x * 10) + 5x * (7 + 5x)) = 0
((70 + 50x) + 5x * (7 + 5x)) = 0
(70 + 50x + (7 * 5x + 5x * 5x)) = 0
(70 + 50x + (35x + 25x2)) = 0

Combine like terms: 50x + 35x = 85x
(70 + 85x + 25x2) = 0

Solving
70 + 85x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(14 + 17x + 5x2) = 0

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

Ignore the factor 5.

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2

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 = {-2, -1.4}

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