10x^2-65x-100=-25

Solution for 10x^2-65x-100=-25 equation:

Simplifying
10x2 + -65x + -100 = -25

Reorder the terms:
-100 + -65x + 10x2 = -25

Solving
-100 + -65x + 10x2 = -25

Solving for variable 'x'.

Reorder the terms:
-100 + 25 + -65x + 10x2 = -25 + 25

Combine like terms: -100 + 25 = -75
-75 + -65x + 10x2 = -25 + 25

Combine like terms: -25 + 25 = 0
-75 + -65x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-15 + -13x + 2x2) = 0

Factor a trinomial.
5((-1 + -1x)(15 + -2x)) = 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 '(15 + -2x)' equal to zero and attempt to solve:

Simplifying
15 + -2x = 0

Solving
15 + -2x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -2x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2x = 0 + -15
-2x = 0 + -15

Combine like terms: 0 + -15 = -15
-2x = -15

Divide each side by '-2'.
x = 7.5

Simplifying
x = 7.5
Solution
x = {-1, 7.5}