2x^2-25x+3x^2+150=180

Solution for 2x^2-25x+3x^2+150=180 equation:

Simplifying
2x2 + -25x + 3x2 + 150 = 180

Reorder the terms:
150 + -25x + 2x2 + 3x2 = 180

Combine like terms: 2x2 + 3x2 = 5x2
150 + -25x + 5x2 = 180

Solving
150 + -25x + 5x2 = 180

Solving for variable 'x'.

Reorder the terms:
150 + -180 + -25x + 5x2 = 180 + -180

Combine like terms: 150 + -180 = -30
-30 + -25x + 5x2 = 180 + -180

Combine like terms: 180 + -180 = 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}