7x^2-42x=-35

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

Simplifying
7x2 + -42x = -35

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

Solving
-42x + 7x2 = -35

Solving for variable 'x'.

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

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

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

Factor a trinomial.
7((1 + -1x)(5 + -1x)) = 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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

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