(6x-15)(3x+20)=(5x-4)(8x+3)-(12+22x^2)

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Solution for (6x-15)(3x+20)=(5x-4)(8x+3)-(12+22x^2) equation: 


Simplifying
(6x + -15)(3x + 20) = (5x + -4)(8x + 3) + -1(12 + 22x2)

Reorder the terms:
(-15 + 6x)(3x + 20) = (5x + -4)(8x + 3) + -1(12 + 22x2)

Reorder the terms:
(-15 + 6x)(20 + 3x) = (5x + -4)(8x + 3) + -1(12 + 22x2)

Multiply (-15 + 6x) * (20 + 3x)
(-15(20 + 3x) + 6x * (20 + 3x)) = (5x + -4)(8x + 3) + -1(12 + 22x2)
((20 * -15 + 3x * -15) + 6x * (20 + 3x)) = (5x + -4)(8x + 3) + -1(12 + 22x2)
((-300 + -45x) + 6x * (20 + 3x)) = (5x + -4)(8x + 3) + -1(12 + 22x2)
(-300 + -45x + (20 * 6x + 3x * 6x)) = (5x + -4)(8x + 3) + -1(12 + 22x2)
(-300 + -45x + (120x + 18x2)) = (5x + -4)(8x + 3) + -1(12 + 22x2)

Combine like terms: -45x + 120x = 75x
(-300 + 75x + 18x2) = (5x + -4)(8x + 3) + -1(12 + 22x2)

Reorder the terms:
-300 + 75x + 18x2 = (-4 + 5x)(8x + 3) + -1(12 + 22x2)

Reorder the terms:
-300 + 75x + 18x2 = (-4 + 5x)(3 + 8x) + -1(12 + 22x2)

Multiply (-4 + 5x) * (3 + 8x)
-300 + 75x + 18x2 = (-4(3 + 8x) + 5x * (3 + 8x)) + -1(12 + 22x2)
-300 + 75x + 18x2 = ((3 * -4 + 8x * -4) + 5x * (3 + 8x)) + -1(12 + 22x2)
-300 + 75x + 18x2 = ((-12 + -32x) + 5x * (3 + 8x)) + -1(12 + 22x2)
-300 + 75x + 18x2 = (-12 + -32x + (3 * 5x + 8x * 5x)) + -1(12 + 22x2)
-300 + 75x + 18x2 = (-12 + -32x + (15x + 40x2)) + -1(12 + 22x2)

Combine like terms: -32x + 15x = -17x
-300 + 75x + 18x2 = (-12 + -17x + 40x2) + -1(12 + 22x2)
-300 + 75x + 18x2 = -12 + -17x + 40x2 + (12 * -1 + 22x2 * -1)
-300 + 75x + 18x2 = -12 + -17x + 40x2 + (-12 + -22x2)

Reorder the terms:
-300 + 75x + 18x2 = -12 + -12 + -17x + 40x2 + -22x2

Combine like terms: -12 + -12 = -24
-300 + 75x + 18x2 = -24 + -17x + 40x2 + -22x2

Combine like terms: 40x2 + -22x2 = 18x2
-300 + 75x + 18x2 = -24 + -17x + 18x2

Add '-18x2' to each side of the equation.
-300 + 75x + 18x2 + -18x2 = -24 + -17x + 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
-300 + 75x + 0 = -24 + -17x + 18x2 + -18x2
-300 + 75x = -24 + -17x + 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
-300 + 75x = -24 + -17x + 0
-300 + 75x = -24 + -17x

Solving
-300 + 75x = -24 + -17x

Solving for variable 'x'.

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

Add '17x' to each side of the equation.
-300 + 75x + 17x = -24 + -17x + 17x

Combine like terms: 75x + 17x = 92x
-300 + 92x = -24 + -17x + 17x

Combine like terms: -17x + 17x = 0
-300 + 92x = -24 + 0
-300 + 92x = -24

Add '300' to each side of the equation.
-300 + 300 + 92x = -24 + 300

Combine like terms: -300 + 300 = 0
0 + 92x = -24 + 300
92x = -24 + 300

Combine like terms: -24 + 300 = 276
92x = 276

Divide each side by '92'.
x = 3

Simplifying
x = 3

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