4(x-2)(x+6)=36

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

Simplifying
4(x + -2)(x + 6) = 36

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

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

Multiply (-2 + x) * (6 + x)
4(-2(6 + x) + x(6 + x)) = 36
4((6 * -2 + x * -2) + x(6 + x)) = 36
4((-12 + -2x) + x(6 + x)) = 36
4(-12 + -2x + (6 * x + x * x)) = 36
4(-12 + -2x + (6x + x2)) = 36

Combine like terms: -2x + 6x = 4x
4(-12 + 4x + x2) = 36
(-12 * 4 + 4x * 4 + x2 * 4) = 36
(-48 + 16x + 4x2) = 36

Solving
-48 + 16x + 4x2 = 36

Solving for variable 'x'.

Reorder the terms:
-48 + -36 + 16x + 4x2 = 36 + -36

Combine like terms: -48 + -36 = -84
-84 + 16x + 4x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-84 + 16x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + 4x + x2) = 0

Factor a trinomial.
4((-7 + -1x)(3 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
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, 3}