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

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

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

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

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

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

Combine like terms: 24x + -6x = 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}