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

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

Simplifying
2(x + -3)(x + 4) = 10x

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

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

Multiply (-3 + x) * (4 + x)
2(-3(4 + x) + x(4 + x)) = 10x
2((4 * -3 + x * -3) + x(4 + x)) = 10x
2((-12 + -3x) + x(4 + x)) = 10x
2(-12 + -3x + (4 * x + x * x)) = 10x
2(-12 + -3x + (4x + x2)) = 10x

Combine like terms: -3x + 4x = 1x
2(-12 + 1x + x2) = 10x
(-12 * 2 + 1x * 2 + x2 * 2) = 10x
(-24 + 2x + 2x2) = 10x

Solving
-24 + 2x + 2x2 = 10x

Solving for variable 'x'.

Reorder the terms:
-24 + 2x + -10x + 2x2 = 10x + -10x

Combine like terms: 2x + -10x = -8x
-24 + -8x + 2x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-24 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -4x + 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}