0=7x^2+35x-42

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

Simplifying
0 = 7x2 + 35x + -42

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

Solving
0 = -42 + 35x + 7x2

Solving for variable 'x'.

Combine like terms: 0 + 42 = 42
42 + -35x + -7x2 = -42 + 35x + 7x2 + 42 + -35x + -7x2

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

Combine like terms: -42 + 42 = 0
42 + -35x + -7x2 = 0 + 35x + -35x + 7x2 + -7x2
42 + -35x + -7x2 = 35x + -35x + 7x2 + -7x2

Combine like terms: 35x + -35x = 0
42 + -35x + -7x2 = 0 + 7x2 + -7x2
42 + -35x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
42 + -35x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(6 + -5x + -1x2) = 0

Factor a trinomial.
7((1 + -1x)(6 + x)) = 0

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

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {1, -6}