4(x^2+x+3)=36

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

Simplifying
4(x2 + x + 3) = 36

Reorder the terms:
4(3 + x + x2) = 36
(3 * 4 + x * 4 + x2 * 4) = 36
(12 + 4x + 4x2) = 36

Solving
12 + 4x + 4x2 = 36

Solving for variable 'x'.

Reorder the terms:
12 + -36 + 4x + 4x2 = 36 + -36

Combine like terms: 12 + -36 = -24
-24 + 4x + 4x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-24 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + x + x2) = 0

Factor a trinomial.
4((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}