4u^2-2=7u

Solution for 4u^2-2=7u equation:

Simplifying
4u2 + -2 = 7u

Reorder the terms:
-2 + 4u2 = 7u

Solving
-2 + 4u2 = 7u

Solving for variable 'u'.

Reorder the terms:
-2 + -7u + 4u2 = 7u + -7u

Combine like terms: 7u + -7u = 0
-2 + -7u + 4u2 = 0

Factor a trinomial.
(-1 + -4u)(2 + -1u) = 0

Subproblem 1
Set the factor '(-1 + -4u)' equal to zero and attempt to solve:

Simplifying
-1 + -4u = 0

Solving
-1 + -4u = 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 + -4u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4u = 0 + 1
-4u = 0 + 1

Combine like terms: 0 + 1 = 1
-4u = 1

Divide each side by '-4'.
u = -0.25

Simplifying
u = -0.25
Subproblem 2
Set the factor '(2 + -1u)' equal to zero and attempt to solve:

Simplifying
2 + -1u = 0

Solving
2 + -1u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1u = 0 + -2
-1u = 0 + -2

Combine like terms: 0 + -2 = -2
-1u = -2

Divide each side by '-1'.
u = 2

Simplifying
u = 2
Solution
u = {-0.25, 2}