7x=4x^2-2

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

Simplifying
7x = 4x2 + -2

Reorder the terms:
7x = -2 + 4x2

Solving
7x = -2 + 4x2

Solving for variable 'x'.

Reorder the terms:
2 + 7x + -4x2 = -2 + 4x2 + 2 + -4x2

Reorder the terms:
2 + 7x + -4x2 = -2 + 2 + 4x2 + -4x2

Combine like terms: -2 + 2 = 0
2 + 7x + -4x2 = 0 + 4x2 + -4x2
2 + 7x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
2 + 7x + -4x2 = 0

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

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

Simplifying
x = 2
Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

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

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

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

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