(4x-3)(2x+6)=500

Solution for (4x-3)(2x+6)=500 equation:

Simplifying
(4x + -3)(2x + 6) = 500

Reorder the terms:
(-3 + 4x)(2x + 6) = 500

Reorder the terms:
(-3 + 4x)(6 + 2x) = 500

Multiply (-3 + 4x) * (6 + 2x)
(-3(6 + 2x) + 4x * (6 + 2x)) = 500
((6 * -3 + 2x * -3) + 4x * (6 + 2x)) = 500
((-18 + -6x) + 4x * (6 + 2x)) = 500
(-18 + -6x + (6 * 4x + 2x * 4x)) = 500
(-18 + -6x + (24x + 8x2)) = 500

Combine like terms: -6x + 24x = 18x
(-18 + 18x + 8x2) = 500

Solving
-18 + 18x + 8x2 = 500

Solving for variable 'x'.

Reorder the terms:
-18 + -500 + 18x + 8x2 = 500 + -500

Combine like terms: -18 + -500 = -518
-518 + 18x + 8x2 = 500 + -500

Combine like terms: 500 + -500 = 0
-518 + 18x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-259 + 9x + 4x2) = 0

Factor a trinomial.
2((-37 + -4x)(7 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-37 + -4x)' equal to zero and attempt to solve:

Simplifying
-37 + -4x = 0

Solving
-37 + -4x = 0

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

Add '37' to each side of the equation.
-37 + 37 + -4x = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -4x = 0 + 37
-4x = 0 + 37

Combine like terms: 0 + 37 = 37
-4x = 37

Divide each side by '-4'.
x = -9.25

Simplifying
x = -9.25
Subproblem 2
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
Solution
x = {-9.25, 7}