3-4(x-5)(3-x)=24-(2x-1)(7-2x)

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Solution for 3-4(x-5)(3-x)=24-(2x-1)(7-2x) equation: 


Simplifying
3 + -4(x + -5)(3 + -1x) = 24 + -1(2x + -1)(7 + -2x)

Reorder the terms:
3 + -4(-5 + x)(3 + -1x) = 24 + -1(2x + -1)(7 + -2x)

Multiply (-5 + x) * (3 + -1x)
3 + -4(-5(3 + -1x) + x(3 + -1x)) = 24 + -1(2x + -1)(7 + -2x)
3 + -4((3 * -5 + -1x * -5) + x(3 + -1x)) = 24 + -1(2x + -1)(7 + -2x)
3 + -4((-15 + 5x) + x(3 + -1x)) = 24 + -1(2x + -1)(7 + -2x)
3 + -4(-15 + 5x + (3 * x + -1x * x)) = 24 + -1(2x + -1)(7 + -2x)
3 + -4(-15 + 5x + (3x + -1x2)) = 24 + -1(2x + -1)(7 + -2x)

Combine like terms: 5x + 3x = 8x
3 + -4(-15 + 8x + -1x2) = 24 + -1(2x + -1)(7 + -2x)
3 + (-15 * -4 + 8x * -4 + -1x2 * -4) = 24 + -1(2x + -1)(7 + -2x)
3 + (60 + -32x + 4x2) = 24 + -1(2x + -1)(7 + -2x)

Combine like terms: 3 + 60 = 63
63 + -32x + 4x2 = 24 + -1(2x + -1)(7 + -2x)

Reorder the terms:
63 + -32x + 4x2 = 24 + -1(-1 + 2x)(7 + -2x)

Multiply (-1 + 2x) * (7 + -2x)
63 + -32x + 4x2 = 24 + -1(-1(7 + -2x) + 2x * (7 + -2x))
63 + -32x + 4x2 = 24 + -1((7 * -1 + -2x * -1) + 2x * (7 + -2x))
63 + -32x + 4x2 = 24 + -1((-7 + 2x) + 2x * (7 + -2x))
63 + -32x + 4x2 = 24 + -1(-7 + 2x + (7 * 2x + -2x * 2x))
63 + -32x + 4x2 = 24 + -1(-7 + 2x + (14x + -4x2))

Combine like terms: 2x + 14x = 16x
63 + -32x + 4x2 = 24 + -1(-7 + 16x + -4x2)
63 + -32x + 4x2 = 24 + (-7 * -1 + 16x * -1 + -4x2 * -1)
63 + -32x + 4x2 = 24 + (7 + -16x + 4x2)

Combine like terms: 24 + 7 = 31
63 + -32x + 4x2 = 31 + -16x + 4x2

Add '-4x2' to each side of the equation.
63 + -32x + 4x2 + -4x2 = 31 + -16x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
63 + -32x + 0 = 31 + -16x + 4x2 + -4x2
63 + -32x = 31 + -16x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
63 + -32x = 31 + -16x + 0
63 + -32x = 31 + -16x

Solving
63 + -32x = 31 + -16x

Solving for variable 'x'.

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

Add '16x' to each side of the equation.
63 + -32x + 16x = 31 + -16x + 16x

Combine like terms: -32x + 16x = -16x
63 + -16x = 31 + -16x + 16x

Combine like terms: -16x + 16x = 0
63 + -16x = 31 + 0
63 + -16x = 31

Add '-63' to each side of the equation.
63 + -63 + -16x = 31 + -63

Combine like terms: 63 + -63 = 0
0 + -16x = 31 + -63
-16x = 31 + -63

Combine like terms: 31 + -63 = -32
-16x = -32

Divide each side by '-16'.
x = 2

Simplifying
x = 2

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