4x(x-3)+x(x+6)=27

Solution for 4x(x-3)+x(x+6)=27 equation:

Simplifying
4x(x + -3) + x(x + 6) = 27

Reorder the terms:
4x(-3 + x) + x(x + 6) = 27
(-3 * 4x + x * 4x) + x(x + 6) = 27
(-12x + 4x2) + x(x + 6) = 27

Reorder the terms:
-12x + 4x2 + x(6 + x) = 27
-12x + 4x2 + (6 * x + x * x) = 27
-12x + 4x2 + (6x + x2) = 27

Reorder the terms:
-12x + 6x + 4x2 + x2 = 27

Combine like terms: -12x + 6x = -6x
-6x + 4x2 + x2 = 27

Combine like terms: 4x2 + x2 = 5x2
-6x + 5x2 = 27

Solving
-6x + 5x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + -6x + 5x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -6x + 5x2 = 0

Factor a trinomial.
(-9 + -5x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -5x)' equal to zero and attempt to solve:

Simplifying
-9 + -5x = 0

Solving
-9 + -5x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -5x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5x = 0 + 9
-5x = 0 + 9

Combine like terms: 0 + 9 = 9
-5x = 9

Divide each side by '-5'.
x = -1.8

Simplifying
x = -1.8
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 = {-1.8, 3}