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

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


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

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

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

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

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

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

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

Combine like terms: 2x + 14x = 16x
63 + -32x + 4x2 = 24 + -2(-7 + 16x + -4x2)
63 + -32x + 4x2 = 24 + (-7 * -2 + 16x * -2 + -4x2 * -2)
63 + -32x + 4x2 = 24 + (14 + -32x + 8x2)

Combine like terms: 24 + 14 = 38
63 + -32x + 4x2 = 38 + -32x + 8x2

Add '32x' to each side of the equation.
63 + -32x + 32x + 4x2 = 38 + -32x + 32x + 8x2

Combine like terms: -32x + 32x = 0
63 + 0 + 4x2 = 38 + -32x + 32x + 8x2
63 + 4x2 = 38 + -32x + 32x + 8x2

Combine like terms: -32x + 32x = 0
63 + 4x2 = 38 + 0 + 8x2
63 + 4x2 = 38 + 8x2

Solving
63 + 4x2 = 38 + 8x2

Solving for variable 'x'.

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

Add '-8x2' to each side of the equation.
63 + 4x2 + -8x2 = 38 + 8x2 + -8x2

Combine like terms: 4x2 + -8x2 = -4x2
63 + -4x2 = 38 + 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
63 + -4x2 = 38 + 0
63 + -4x2 = 38

Add '-63' to each side of the equation.
63 + -63 + -4x2 = 38 + -63

Combine like terms: 63 + -63 = 0
0 + -4x2 = 38 + -63
-4x2 = 38 + -63

Combine like terms: 38 + -63 = -25
-4x2 = -25

Divide each side by '-4'.
x2 = 6.25

Simplifying
x2 = 6.25

Take the square root of each side:
x = {-2.5, 2.5}

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