10=5x^2-7x+4

Solution for 10=5x^2-7x+4 equation:

Simplifying
10 = 5x2 + -7x + 4

Reorder the terms:
10 = 4 + -7x + 5x2

Solving
10 = 4 + -7x + 5x2

Solving for variable 'x'.

Combine like terms: 10 + -4 = 6
6 + 7x + -5x2 = 4 + -7x + 5x2 + -4 + 7x + -5x2

Reorder the terms:
6 + 7x + -5x2 = 4 + -4 + -7x + 7x + 5x2 + -5x2

Combine like terms: 4 + -4 = 0
6 + 7x + -5x2 = 0 + -7x + 7x + 5x2 + -5x2
6 + 7x + -5x2 = -7x + 7x + 5x2 + -5x2

Combine like terms: -7x + 7x = 0
6 + 7x + -5x2 = 0 + 5x2 + -5x2
6 + 7x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
6 + 7x + -5x2 = 0

Factor a trinomial.
(2 + -1x)(3 + 5x) = 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 '(3 + 5x)' equal to zero and attempt to solve:

Simplifying
3 + 5x = 0

Solving
3 + 5x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5x = 0 + -3
5x = 0 + -3

Combine like terms: 0 + -3 = -3
5x = -3

Divide each side by '5'.
x = -0.6

Simplifying
x = -0.6
Solution
x = {2, -0.6}