100=-15x^2+75x+10

Solution for 100=-15x^2+75x+10 equation:

Simplifying
100 = -15x2 + 75x + 10

Reorder the terms:
100 = 10 + 75x + -15x2

Solving
100 = 10 + 75x + -15x2

Solving for variable 'x'.

Combine like terms: 100 + -10 = 90
90 + -75x + 15x2 = 10 + 75x + -15x2 + -10 + -75x + 15x2

Reorder the terms:
90 + -75x + 15x2 = 10 + -10 + 75x + -75x + -15x2 + 15x2

Combine like terms: 10 + -10 = 0
90 + -75x + 15x2 = 0 + 75x + -75x + -15x2 + 15x2
90 + -75x + 15x2 = 75x + -75x + -15x2 + 15x2

Combine like terms: 75x + -75x = 0
90 + -75x + 15x2 = 0 + -15x2 + 15x2
90 + -75x + 15x2 = -15x2 + 15x2

Combine like terms: -15x2 + 15x2 = 0
90 + -75x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(6 + -5x + x2) = 0

Factor a trinomial.
15((2 + -1x)(3 + -1x)) = 0

Ignore the factor 15.
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}