2x^2+90x+1000=1612

Solution for 2x^2+90x+1000=1612 equation:

Simplifying
2x2 + 90x + 1000 = 1612

Reorder the terms:
1000 + 90x + 2x2 = 1612

Solving
1000 + 90x + 2x2 = 1612

Solving for variable 'x'.

Reorder the terms:
1000 + -1612 + 90x + 2x2 = 1612 + -1612

Combine like terms: 1000 + -1612 = -612
-612 + 90x + 2x2 = 1612 + -1612

Combine like terms: 1612 + -1612 = 0
-612 + 90x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-306 + 45x + x2) = 0

Factor a trinomial.
2((-51 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-51 + -1x)' equal to zero and attempt to solve:

Simplifying
-51 + -1x = 0

Solving
-51 + -1x = 0

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

Add '51' to each side of the equation.
-51 + 51 + -1x = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -1x = 0 + 51
-1x = 0 + 51

Combine like terms: 0 + 51 = 51
-1x = 51

Divide each side by '-1'.
x = -51

Simplifying
x = -51
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 = {-51, 6}