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

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Solution for 12-2(x-1)2=4(x-2)-(x-3)(2x-5) equation:


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

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

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

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

Combine like terms: 12 + 4 = 16
16 + -4x = 4(x + -2) + -1(x + -3)(2x + -5)

Reorder the terms:
16 + -4x = 4(-2 + x) + -1(x + -3)(2x + -5)
16 + -4x = (-2 * 4 + x * 4) + -1(x + -3)(2x + -5)
16 + -4x = (-8 + 4x) + -1(x + -3)(2x + -5)

Reorder the terms:
16 + -4x = -8 + 4x + -1(-3 + x)(2x + -5)

Reorder the terms:
16 + -4x = -8 + 4x + -1(-3 + x)(-5 + 2x)

Multiply (-3 + x) * (-5 + 2x)
16 + -4x = -8 + 4x + -1(-3(-5 + 2x) + x(-5 + 2x))
16 + -4x = -8 + 4x + -1((-5 * -3 + 2x * -3) + x(-5 + 2x))
16 + -4x = -8 + 4x + -1((15 + -6x) + x(-5 + 2x))
16 + -4x = -8 + 4x + -1(15 + -6x + (-5 * x + 2x * x))
16 + -4x = -8 + 4x + -1(15 + -6x + (-5x + 2x2))

Combine like terms: -6x + -5x = -11x
16 + -4x = -8 + 4x + -1(15 + -11x + 2x2)
16 + -4x = -8 + 4x + (15 * -1 + -11x * -1 + 2x2 * -1)
16 + -4x = -8 + 4x + (-15 + 11x + -2x2)

Reorder the terms:
16 + -4x = -8 + -15 + 4x + 11x + -2x2

Combine like terms: -8 + -15 = -23
16 + -4x = -23 + 4x + 11x + -2x2

Combine like terms: 4x + 11x = 15x
16 + -4x = -23 + 15x + -2x2

Solving
16 + -4x = -23 + 15x + -2x2

Solving for variable 'x'.

Reorder the terms:
16 + 23 + -4x + -15x + 2x2 = -23 + 15x + -2x2 + 23 + -15x + 2x2

Combine like terms: 16 + 23 = 39
39 + -4x + -15x + 2x2 = -23 + 15x + -2x2 + 23 + -15x + 2x2

Combine like terms: -4x + -15x = -19x
39 + -19x + 2x2 = -23 + 15x + -2x2 + 23 + -15x + 2x2

Reorder the terms:
39 + -19x + 2x2 = -23 + 23 + 15x + -15x + -2x2 + 2x2

Combine like terms: -23 + 23 = 0
39 + -19x + 2x2 = 0 + 15x + -15x + -2x2 + 2x2
39 + -19x + 2x2 = 15x + -15x + -2x2 + 2x2

Combine like terms: 15x + -15x = 0
39 + -19x + 2x2 = 0 + -2x2 + 2x2
39 + -19x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
39 + -19x + 2x2 = 0

Factor a trinomial.
(3 + -1x)(13 + -2x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(13 + -2x)' equal to zero and attempt to solve:

Simplifying
13 + -2x = 0

Solving
13 + -2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2x = 0 + -13
-2x = 0 + -13

Combine like terms: 0 + -13 = -13
-2x = -13

Divide each side by '-2'.
x = 6.5

Simplifying
x = 6.5
Solution
x = {3, 6.5}

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