(2x+7)(2x+10)=0

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Solution for (2x+7)(2x+10)=0 equation: 


Simplifying
(2x + 7)(2x + 10) = 0

Reorder the terms:
(7 + 2x)(2x + 10) = 0

Reorder the terms:
(7 + 2x)(10 + 2x) = 0

Multiply (7 + 2x) * (10 + 2x)
(7(10 + 2x) + 2x * (10 + 2x)) = 0
((10 * 7 + 2x * 7) + 2x * (10 + 2x)) = 0
((70 + 14x) + 2x * (10 + 2x)) = 0
(70 + 14x + (10 * 2x + 2x * 2x)) = 0
(70 + 14x + (20x + 4x2)) = 0

Combine like terms: 14x + 20x = 34x
(70 + 34x + 4x2) = 0

Solving
70 + 34x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + 17x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

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

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

Simplifying
x = -5

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 = {-5, -3.5}

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