(2x-3)(3x-4)-(x-13)(x-4)=40

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Solution for (2x-3)(3x-4)-(x-13)(x-4)=40 equation: 


Simplifying
(2x + -3)(3x + -4) + -1(x + -13)(x + -4) = 40

Reorder the terms:
(-3 + 2x)(3x + -4) + -1(x + -13)(x + -4) = 40

Reorder the terms:
(-3 + 2x)(-4 + 3x) + -1(x + -13)(x + -4) = 40

Multiply (-3 + 2x) * (-4 + 3x)
(-3(-4 + 3x) + 2x * (-4 + 3x)) + -1(x + -13)(x + -4) = 40
((-4 * -3 + 3x * -3) + 2x * (-4 + 3x)) + -1(x + -13)(x + -4) = 40
((12 + -9x) + 2x * (-4 + 3x)) + -1(x + -13)(x + -4) = 40
(12 + -9x + (-4 * 2x + 3x * 2x)) + -1(x + -13)(x + -4) = 40
(12 + -9x + (-8x + 6x2)) + -1(x + -13)(x + -4) = 40

Combine like terms: -9x + -8x = -17x
(12 + -17x + 6x2) + -1(x + -13)(x + -4) = 40

Reorder the terms:
12 + -17x + 6x2 + -1(-13 + x)(x + -4) = 40

Reorder the terms:
12 + -17x + 6x2 + -1(-13 + x)(-4 + x) = 40

Multiply (-13 + x) * (-4 + x)
12 + -17x + 6x2 + -1(-13(-4 + x) + x(-4 + x)) = 40
12 + -17x + 6x2 + -1((-4 * -13 + x * -13) + x(-4 + x)) = 40
12 + -17x + 6x2 + -1((52 + -13x) + x(-4 + x)) = 40
12 + -17x + 6x2 + -1(52 + -13x + (-4 * x + x * x)) = 40
12 + -17x + 6x2 + -1(52 + -13x + (-4x + x2)) = 40

Combine like terms: -13x + -4x = -17x
12 + -17x + 6x2 + -1(52 + -17x + x2) = 40
12 + -17x + 6x2 + (52 * -1 + -17x * -1 + x2 * -1) = 40
12 + -17x + 6x2 + (-52 + 17x + -1x2) = 40

Reorder the terms:
12 + -52 + -17x + 17x + 6x2 + -1x2 = 40

Combine like terms: 12 + -52 = -40
-40 + -17x + 17x + 6x2 + -1x2 = 40

Combine like terms: -17x + 17x = 0
-40 + 0 + 6x2 + -1x2 = 40
-40 + 6x2 + -1x2 = 40

Combine like terms: 6x2 + -1x2 = 5x2
-40 + 5x2 = 40

Solving
-40 + 5x2 = 40

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + 5x2 = 40 + 40

Combine like terms: -40 + 40 = 0
0 + 5x2 = 40 + 40
5x2 = 40 + 40

Combine like terms: 40 + 40 = 80
5x2 = 80

Divide each side by '5'.
x2 = 16

Simplifying
x2 = 16

Take the square root of each side:
x = {-4, 4}

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