2x(x+5)+7(x+5)=0

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Solution for 2x(x+5)+7(x+5)=0 equation: 


Simplifying
2x(x + 5) + 7(x + 5) = 0

Reorder the terms:
2x(5 + x) + 7(x + 5) = 0
(5 * 2x + x * 2x) + 7(x + 5) = 0
(10x + 2x2) + 7(x + 5) = 0

Reorder the terms:
10x + 2x2 + 7(5 + x) = 0
10x + 2x2 + (5 * 7 + x * 7) = 0
10x + 2x2 + (35 + 7x) = 0

Reorder the terms:
35 + 10x + 7x + 2x2 = 0

Combine like terms: 10x + 7x = 17x
35 + 17x + 2x2 = 0

Solving
35 + 17x + 2x2 = 0

Solving for variable 'x'.

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


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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