(2x^2-25x)+(3x^2+60)=90

Solution for (2x^2-25x)+(3x^2+60)=90 equation:

Simplifying
(2x2 + -25x) + (3x2 + 60) = 90

Reorder the terms:
(-25x + 2x2) + (3x2 + 60) = 90

Remove parenthesis around (-25x + 2x2)
-25x + 2x2 + (3x2 + 60) = 90

Reorder the terms:
-25x + 2x2 + (60 + 3x2) = 90

Remove parenthesis around (60 + 3x2)
-25x + 2x2 + 60 + 3x2 = 90

Reorder the terms:
60 + -25x + 2x2 + 3x2 = 90

Combine like terms: 2x2 + 3x2 = 5x2
60 + -25x + 5x2 = 90

Solving
60 + -25x + 5x2 = 90

Solving for variable 'x'.

Reorder the terms:
60 + -90 + -25x + 5x2 = 90 + -90

Combine like terms: 60 + -90 = -30
-30 + -25x + 5x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-30 + -25x + 5x2 = 0

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

Factor a trinomial.
5((-1 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-1, 6}