5x^2-25x+37=7

Solution for 5x^2-25x+37=7 equation:

Simplifying
5x2 + -25x + 37 = 7

Reorder the terms:
37 + -25x + 5x2 = 7

Solving
37 + -25x + 5x2 = 7

Solving for variable 'x'.

Reorder the terms:
37 + -7 + -25x + 5x2 = 7 + -7

Combine like terms: 37 + -7 = 30
30 + -25x + 5x2 = 7 + -7

Combine like terms: 7 + -7 = 0
30 + -25x + 5x2 = 0

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

Factor a trinomial.
5((2 + -1x)(3 + -1x)) = 0

Ignore the factor 5.
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 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2, 3}