2(x+4)(x-4)-2(x-3)=6(2x-5)-2(10-x)

Solution for 2(x+4)(x-4)-2(x-3)=6(2x-5)-2(10-x) equation:

Simplifying
2(x + 4)(x + -4) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)

Reorder the terms:
2(4 + x)(x + -4) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)

Reorder the terms:
2(4 + x)(-4 + x) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)

Multiply (4 + x) * (-4 + x)
2(4(-4 + x) + x(-4 + x)) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)
2((-4 * 4 + x * 4) + x(-4 + x)) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)
2((-16 + 4x) + x(-4 + x)) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)
2(-16 + 4x + (-4 * x + x * x)) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)
2(-16 + 4x + (-4x + x2)) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)

Combine like terms: 4x + -4x = 0
2(-16 + 0 + x2) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)
2(-16 + x2) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)
(-16 * 2 + x2 * 2) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)
(-32 + 2x2) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x)

Reorder the terms:
-32 + 2x2 + -2(-3 + x) = 6(2x + -5) + -2(10 + -1x)
-32 + 2x2 + (-3 * -2 + x * -2) = 6(2x + -5) + -2(10 + -1x)
-32 + 2x2 + (6 + -2x) = 6(2x + -5) + -2(10 + -1x)

Reorder the terms:
-32 + 6 + -2x + 2x2 = 6(2x + -5) + -2(10 + -1x)

Combine like terms: -32 + 6 = -26
-26 + -2x + 2x2 = 6(2x + -5) + -2(10 + -1x)

Reorder the terms:
-26 + -2x + 2x2 = 6(-5 + 2x) + -2(10 + -1x)
-26 + -2x + 2x2 = (-5 * 6 + 2x * 6) + -2(10 + -1x)
-26 + -2x + 2x2 = (-30 + 12x) + -2(10 + -1x)
-26 + -2x + 2x2 = -30 + 12x + (10 * -2 + -1x * -2)
-26 + -2x + 2x2 = -30 + 12x + (-20 + 2x)

Reorder the terms:
-26 + -2x + 2x2 = -30 + -20 + 12x + 2x

Combine like terms: -30 + -20 = -50
-26 + -2x + 2x2 = -50 + 12x + 2x

Combine like terms: 12x + 2x = 14x
-26 + -2x + 2x2 = -50 + 14x

Solving
-26 + -2x + 2x2 = -50 + 14x

Solving for variable 'x'.

Reorder the terms:
-26 + 50 + -2x + -14x + 2x2 = -50 + 14x + 50 + -14x

Combine like terms: -26 + 50 = 24
24 + -2x + -14x + 2x2 = -50 + 14x + 50 + -14x

Combine like terms: -2x + -14x = -16x
24 + -16x + 2x2 = -50 + 14x + 50 + -14x

Reorder the terms:
24 + -16x + 2x2 = -50 + 50 + 14x + -14x

Combine like terms: -50 + 50 = 0
24 + -16x + 2x2 = 0 + 14x + -14x
24 + -16x + 2x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
24 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -8x + x2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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, 6}