7u^2-42=35u

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

Simplifying
7u2 + -42 = 35u

Reorder the terms:
-42 + 7u2 = 35u

Solving
-42 + 7u2 = 35u

Solving for variable 'u'.

Reorder the terms:
-42 + -35u + 7u2 = 35u + -35u

Combine like terms: 35u + -35u = 0
-42 + -35u + 7u2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + -5u + u2) = 0

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

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

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1u = 0 + 1

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

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

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

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

Simplifying
6 + -1u = 0

Solving
6 + -1u = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
u = 6

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