4x(x+4.5)=90

Solution for 4x(x+4.5)=90 equation:

Simplifying
4x(x + 4.5) = 90

Reorder the terms:
4x(4.5 + x) = 90
(4.5 * 4x + x * 4x) = 90
(18x + 4x2) = 90

Solving
18x + 4x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + 18x + 4x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 9x + 2x2) = 0

Factor a trinomial.
2((-15 + -2x)(3 + -1x)) = 0

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

Simplifying
-15 + -2x = 0

Solving
-15 + -2x = 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 + -2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x = 0 + 15
-2x = 0 + 15

Combine like terms: 0 + 15 = 15
-2x = 15

Divide each side by '-2'.
x = -7.5

Simplifying
x = -7.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-7.5, 3}