(4x)(x)+(x+3)(2x)=180

Solution for (4x)(x)+(x+3)(2x)=180 equation:

Simplifying
(4x)(x) + (x + 3)(2x) = 180

Remove parenthesis around (4x)
4x(x) + (x + 3)(2x) = 180

Multiply x * x
4x2 + (x + 3)(2x) = 180

Reorder the terms:
4x2 + (3 + x)(2x) = 180

Remove parenthesis around (2x)
4x2 + (3 + x) * 2x = 180

Reorder the terms for easier multiplication:
4x2 + 2x(3 + x) = 180
4x2 + (3 * 2x + x * 2x) = 180
4x2 + (6x + 2x2) = 180

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

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

Solving
6x + 6x2 = 180

Solving for variable 'x'.

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

Combine like terms: 180 + -180 = 0
-180 + 6x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + x + x2) = 0

Factor a trinomial.
6((-6 + -1x)(5 + -1x)) = 0

Ignore the factor 6.
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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}