12=4(x-2)-(x-3)(2x-5)

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Solution for 12=4(x-2)-(x-3)(2x-5) equation:


Simplifying
12 = 4(x + -2) + -1(x + -3)(2x + -5)

Reorder the terms:
12 = 4(-2 + x) + -1(x + -3)(2x + -5)
12 = (-2 * 4 + x * 4) + -1(x + -3)(2x + -5)
12 = (-8 + 4x) + -1(x + -3)(2x + -5)

Reorder the terms:
12 = -8 + 4x + -1(-3 + x)(2x + -5)

Reorder the terms:
12 = -8 + 4x + -1(-3 + x)(-5 + 2x)

Multiply (-3 + x) * (-5 + 2x)
12 = -8 + 4x + -1(-3(-5 + 2x) + x(-5 + 2x))
12 = -8 + 4x + -1((-5 * -3 + 2x * -3) + x(-5 + 2x))
12 = -8 + 4x + -1((15 + -6x) + x(-5 + 2x))
12 = -8 + 4x + -1(15 + -6x + (-5 * x + 2x * x))
12 = -8 + 4x + -1(15 + -6x + (-5x + 2x2))

Combine like terms: -6x + -5x = -11x
12 = -8 + 4x + -1(15 + -11x + 2x2)
12 = -8 + 4x + (15 * -1 + -11x * -1 + 2x2 * -1)
12 = -8 + 4x + (-15 + 11x + -2x2)

Reorder the terms:
12 = -8 + -15 + 4x + 11x + -2x2

Combine like terms: -8 + -15 = -23
12 = -23 + 4x + 11x + -2x2

Combine like terms: 4x + 11x = 15x
12 = -23 + 15x + -2x2

Solving
12 = -23 + 15x + -2x2

Solving for variable 'x'.

Combine like terms: 12 + 23 = 35
35 + -15x + 2x2 = -23 + 15x + -2x2 + 23 + -15x + 2x2

Reorder the terms:
35 + -15x + 2x2 = -23 + 23 + 15x + -15x + -2x2 + 2x2

Combine like terms: -23 + 23 = 0
35 + -15x + 2x2 = 0 + 15x + -15x + -2x2 + 2x2
35 + -15x + 2x2 = 15x + -15x + -2x2 + 2x2

Combine like terms: 15x + -15x = 0
35 + -15x + 2x2 = 0 + -2x2 + 2x2
35 + -15x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
35 + -15x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
17.5 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-17.5' to each side of the equation.
17.5 + -7.5x + -17.5 + x2 = 0 + -17.5

Reorder the terms:
17.5 + -17.5 + -7.5x + x2 = 0 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + -7.5x + x2 = 0 + -17.5
-7.5x + x2 = 0 + -17.5

Combine like terms: 0 + -17.5 = -17.5
-7.5x + x2 = -17.5

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -17.5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -17.5 + 14.0625

Combine like terms: -17.5 + 14.0625 = -3.4375
14.0625 + -7.5x + x2 = -3.4375

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = -3.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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