7x^2+42x+35=0

Solution for 7x^2+42x+35=0 equation:

Simplifying
7x2 + 42x + 35 = 0

Reorder the terms:
35 + 42x + 7x2 = 0

Solving
35 + 42x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(5 + 6x + x2) = 0

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

Ignore the factor 7.
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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-5, -1}