5x^2-5x=10

Solution for 5x^2-5x=10 equation:

Simplifying
5x2 + -5x = 10

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

Solving
-5x + 5x2 = 10

Solving for variable 'x'.

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

Combine like terms: 10 + -10 = 0
-10 + -5x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + -1x + x2) = 0

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

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 2
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
Solution
x = {-1, 2}