7x^2+27x-90=0

Solution for 7x^2+27x-90=0 equation:

Simplifying
7x2 + 27x + -90 = 0

Reorder the terms:
-90 + 27x + 7x2 = 0

Solving
-90 + 27x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(15 + -7x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(15 + -7x)' equal to zero and attempt to solve:

Simplifying
15 + -7x = 0

Solving
15 + -7x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -7x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -7x = 0 + -15
-7x = 0 + -15

Combine like terms: 0 + -15 = -15
-7x = -15

Divide each side by '-7'.
x = 2.142857143

Simplifying
x = 2.142857143
Solution
x = {-6, 2.142857143}