(4x^2-6)+(-2x^2+19x)=180

Solution for (4x^2-6)+(-2x^2+19x)=180 equation:

Simplifying
(4x2 + -6) + (-2x2 + 19x) = 180

Reorder the terms:
(-6 + 4x2) + (-2x2 + 19x) = 180

Remove parenthesis around (-6 + 4x2)
-6 + 4x2 + (-2x2 + 19x) = 180

Reorder the terms:
-6 + 4x2 + (19x + -2x2) = 180

Remove parenthesis around (19x + -2x2)
-6 + 4x2 + 19x + -2x2 = 180

Reorder the terms:
-6 + 19x + 4x2 + -2x2 = 180

Combine like terms: 4x2 + -2x2 = 2x2
-6 + 19x + 2x2 = 180

Solving
-6 + 19x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-6 + -180 + 19x + 2x2 = 180 + -180

Combine like terms: -6 + -180 = -186
-186 + 19x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-186 + 19x + 2x2 = 0

Factor a trinomial.
(-31 + -2x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-31 + -2x)' equal to zero and attempt to solve:

Simplifying
-31 + -2x = 0

Solving
-31 + -2x = 0

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

Add '31' to each side of the equation.
-31 + 31 + -2x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -2x = 0 + 31
-2x = 0 + 31

Combine like terms: 0 + 31 = 31
-2x = 31

Divide each side by '-2'.
x = -15.5

Simplifying
x = -15.5
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 = {-15.5, 6}