(3x-4)(4x-3)-(2x-7)(3x-2)=214

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Solution for (3x-4)(4x-3)-(2x-7)(3x-2)=214 equation: 


Simplifying
(3x + -4)(4x + -3) + -1(2x + -7)(3x + -2) = 214

Reorder the terms:
(-4 + 3x)(4x + -3) + -1(2x + -7)(3x + -2) = 214

Reorder the terms:
(-4 + 3x)(-3 + 4x) + -1(2x + -7)(3x + -2) = 214

Multiply (-4 + 3x) * (-3 + 4x)
(-4(-3 + 4x) + 3x * (-3 + 4x)) + -1(2x + -7)(3x + -2) = 214
((-3 * -4 + 4x * -4) + 3x * (-3 + 4x)) + -1(2x + -7)(3x + -2) = 214
((12 + -16x) + 3x * (-3 + 4x)) + -1(2x + -7)(3x + -2) = 214
(12 + -16x + (-3 * 3x + 4x * 3x)) + -1(2x + -7)(3x + -2) = 214
(12 + -16x + (-9x + 12x2)) + -1(2x + -7)(3x + -2) = 214

Combine like terms: -16x + -9x = -25x
(12 + -25x + 12x2) + -1(2x + -7)(3x + -2) = 214

Reorder the terms:
12 + -25x + 12x2 + -1(-7 + 2x)(3x + -2) = 214

Reorder the terms:
12 + -25x + 12x2 + -1(-7 + 2x)(-2 + 3x) = 214

Multiply (-7 + 2x) * (-2 + 3x)
12 + -25x + 12x2 + -1(-7(-2 + 3x) + 2x * (-2 + 3x)) = 214
12 + -25x + 12x2 + -1((-2 * -7 + 3x * -7) + 2x * (-2 + 3x)) = 214
12 + -25x + 12x2 + -1((14 + -21x) + 2x * (-2 + 3x)) = 214
12 + -25x + 12x2 + -1(14 + -21x + (-2 * 2x + 3x * 2x)) = 214
12 + -25x + 12x2 + -1(14 + -21x + (-4x + 6x2)) = 214

Combine like terms: -21x + -4x = -25x
12 + -25x + 12x2 + -1(14 + -25x + 6x2) = 214
12 + -25x + 12x2 + (14 * -1 + -25x * -1 + 6x2 * -1) = 214
12 + -25x + 12x2 + (-14 + 25x + -6x2) = 214

Reorder the terms:
12 + -14 + -25x + 25x + 12x2 + -6x2 = 214

Combine like terms: 12 + -14 = -2
-2 + -25x + 25x + 12x2 + -6x2 = 214

Combine like terms: -25x + 25x = 0
-2 + 0 + 12x2 + -6x2 = 214
-2 + 12x2 + -6x2 = 214

Combine like terms: 12x2 + -6x2 = 6x2
-2 + 6x2 = 214

Solving
-2 + 6x2 = 214

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + 6x2 = 214 + 2

Combine like terms: -2 + 2 = 0
0 + 6x2 = 214 + 2
6x2 = 214 + 2

Combine like terms: 214 + 2 = 216
6x2 = 216

Divide each side by '6'.
x2 = 36

Simplifying
x2 = 36

Take the square root of each side:
x = {-6, 6}

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