(x-6)(3+4x)+2(x^2-36)=0

Solution for (x-6)(3+4x)+2(x^2-36)=0 equation:

Simplifying
(x + -6)(3 + 4x) + 2(x2 + -36) = 0

Reorder the terms:
(-6 + x)(3 + 4x) + 2(x2 + -36) = 0

Multiply (-6 + x) * (3 + 4x)
(-6(3 + 4x) + x(3 + 4x)) + 2(x2 + -36) = 0
((3 * -6 + 4x * -6) + x(3 + 4x)) + 2(x2 + -36) = 0
((-18 + -24x) + x(3 + 4x)) + 2(x2 + -36) = 0
(-18 + -24x + (3 * x + 4x * x)) + 2(x2 + -36) = 0
(-18 + -24x + (3x + 4x2)) + 2(x2 + -36) = 0

Combine like terms: -24x + 3x = -21x
(-18 + -21x + 4x2) + 2(x2 + -36) = 0

Reorder the terms:
-18 + -21x + 4x2 + 2(-36 + x2) = 0
-18 + -21x + 4x2 + (-36 * 2 + x2 * 2) = 0
-18 + -21x + 4x2 + (-72 + 2x2) = 0

Reorder the terms:
-18 + -72 + -21x + 4x2 + 2x2 = 0

Combine like terms: -18 + -72 = -90
-90 + -21x + 4x2 + 2x2 = 0

Combine like terms: 4x2 + 2x2 = 6x2
-90 + -21x + 6x2 = 0

Solving
-90 + -21x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + -7x + 2x2) = 0

Factor a trinomial.
3((-5 + -2x)(6 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
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 = {-2.5, 6}