(2x-3)(x-4)+(x+4)(2x-3)=0

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Solution for (2x-3)(x-4)+(x+4)(2x-3)=0 equation: 


Simplifying
(2x + -3)(x + -4) + (x + 4)(2x + -3) = 0

Reorder the terms:
(-3 + 2x)(x + -4) + (x + 4)(2x + -3) = 0

Reorder the terms:
(-3 + 2x)(-4 + x) + (x + 4)(2x + -3) = 0

Multiply (-3 + 2x) * (-4 + x)
(-3(-4 + x) + 2x * (-4 + x)) + (x + 4)(2x + -3) = 0
((-4 * -3 + x * -3) + 2x * (-4 + x)) + (x + 4)(2x + -3) = 0
((12 + -3x) + 2x * (-4 + x)) + (x + 4)(2x + -3) = 0
(12 + -3x + (-4 * 2x + x * 2x)) + (x + 4)(2x + -3) = 0
(12 + -3x + (-8x + 2x2)) + (x + 4)(2x + -3) = 0

Combine like terms: -3x + -8x = -11x
(12 + -11x + 2x2) + (x + 4)(2x + -3) = 0

Reorder the terms:
12 + -11x + 2x2 + (4 + x)(2x + -3) = 0

Reorder the terms:
12 + -11x + 2x2 + (4 + x)(-3 + 2x) = 0

Multiply (4 + x) * (-3 + 2x)
12 + -11x + 2x2 + (4(-3 + 2x) + x(-3 + 2x)) = 0
12 + -11x + 2x2 + ((-3 * 4 + 2x * 4) + x(-3 + 2x)) = 0
12 + -11x + 2x2 + ((-12 + 8x) + x(-3 + 2x)) = 0
12 + -11x + 2x2 + (-12 + 8x + (-3 * x + 2x * x)) = 0
12 + -11x + 2x2 + (-12 + 8x + (-3x + 2x2)) = 0

Combine like terms: 8x + -3x = 5x
12 + -11x + 2x2 + (-12 + 5x + 2x2) = 0

Reorder the terms:
12 + -12 + -11x + 5x + 2x2 + 2x2 = 0

Combine like terms: 12 + -12 = 0
0 + -11x + 5x + 2x2 + 2x2 = 0
-11x + 5x + 2x2 + 2x2 = 0

Combine like terms: -11x + 5x = -6x
-6x + 2x2 + 2x2 = 0

Combine like terms: 2x2 + 2x2 = 4x2
-6x + 4x2 = 0

Solving
-6x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3 + 2x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 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 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, 1.5}

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