(2x+4)(x+3)-(x-7)(x-3)=(x-3)(-10x-15)

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Solution for (2x+4)(x+3)-(x-7)(x-3)=(x-3)(-10x-15) equation:


Simplifying
(2x + 4)(x + 3) + -1(x + -7)(x + -3) = (x + -3)(-10x + -15)

Reorder the terms:
(4 + 2x)(x + 3) + -1(x + -7)(x + -3) = (x + -3)(-10x + -15)

Reorder the terms:
(4 + 2x)(3 + x) + -1(x + -7)(x + -3) = (x + -3)(-10x + -15)

Multiply (4 + 2x) * (3 + x)
(4(3 + x) + 2x * (3 + x)) + -1(x + -7)(x + -3) = (x + -3)(-10x + -15)
((3 * 4 + x * 4) + 2x * (3 + x)) + -1(x + -7)(x + -3) = (x + -3)(-10x + -15)
((12 + 4x) + 2x * (3 + x)) + -1(x + -7)(x + -3) = (x + -3)(-10x + -15)
(12 + 4x + (3 * 2x + x * 2x)) + -1(x + -7)(x + -3) = (x + -3)(-10x + -15)
(12 + 4x + (6x + 2x2)) + -1(x + -7)(x + -3) = (x + -3)(-10x + -15)

Combine like terms: 4x + 6x = 10x
(12 + 10x + 2x2) + -1(x + -7)(x + -3) = (x + -3)(-10x + -15)

Reorder the terms:
12 + 10x + 2x2 + -1(-7 + x)(x + -3) = (x + -3)(-10x + -15)

Reorder the terms:
12 + 10x + 2x2 + -1(-7 + x)(-3 + x) = (x + -3)(-10x + -15)

Multiply (-7 + x) * (-3 + x)
12 + 10x + 2x2 + -1(-7(-3 + x) + x(-3 + x)) = (x + -3)(-10x + -15)
12 + 10x + 2x2 + -1((-3 * -7 + x * -7) + x(-3 + x)) = (x + -3)(-10x + -15)
12 + 10x + 2x2 + -1((21 + -7x) + x(-3 + x)) = (x + -3)(-10x + -15)
12 + 10x + 2x2 + -1(21 + -7x + (-3 * x + x * x)) = (x + -3)(-10x + -15)
12 + 10x + 2x2 + -1(21 + -7x + (-3x + x2)) = (x + -3)(-10x + -15)

Combine like terms: -7x + -3x = -10x
12 + 10x + 2x2 + -1(21 + -10x + x2) = (x + -3)(-10x + -15)
12 + 10x + 2x2 + (21 * -1 + -10x * -1 + x2 * -1) = (x + -3)(-10x + -15)
12 + 10x + 2x2 + (-21 + 10x + -1x2) = (x + -3)(-10x + -15)

Reorder the terms:
12 + -21 + 10x + 10x + 2x2 + -1x2 = (x + -3)(-10x + -15)

Combine like terms: 12 + -21 = -9
-9 + 10x + 10x + 2x2 + -1x2 = (x + -3)(-10x + -15)

Combine like terms: 10x + 10x = 20x
-9 + 20x + 2x2 + -1x2 = (x + -3)(-10x + -15)

Combine like terms: 2x2 + -1x2 = 1x2
-9 + 20x + 1x2 = (x + -3)(-10x + -15)

Reorder the terms:
-9 + 20x + 1x2 = (-3 + x)(-10x + -15)

Reorder the terms:
-9 + 20x + 1x2 = (-3 + x)(-15 + -10x)

Multiply (-3 + x) * (-15 + -10x)
-9 + 20x + 1x2 = (-3(-15 + -10x) + x(-15 + -10x))
-9 + 20x + 1x2 = ((-15 * -3 + -10x * -3) + x(-15 + -10x))
-9 + 20x + 1x2 = ((45 + 30x) + x(-15 + -10x))
-9 + 20x + 1x2 = (45 + 30x + (-15 * x + -10x * x))
-9 + 20x + 1x2 = (45 + 30x + (-15x + -10x2))

Combine like terms: 30x + -15x = 15x
-9 + 20x + 1x2 = (45 + 15x + -10x2)

Solving
-9 + 20x + 1x2 = 45 + 15x + -10x2

Solving for variable 'x'.

Reorder the terms:
-9 + -45 + 20x + -15x + 1x2 + 10x2 = 45 + 15x + -10x2 + -45 + -15x + 10x2

Combine like terms: -9 + -45 = -54
-54 + 20x + -15x + 1x2 + 10x2 = 45 + 15x + -10x2 + -45 + -15x + 10x2

Combine like terms: 20x + -15x = 5x
-54 + 5x + 1x2 + 10x2 = 45 + 15x + -10x2 + -45 + -15x + 10x2

Combine like terms: 1x2 + 10x2 = 11x2
-54 + 5x + 11x2 = 45 + 15x + -10x2 + -45 + -15x + 10x2

Reorder the terms:
-54 + 5x + 11x2 = 45 + -45 + 15x + -15x + -10x2 + 10x2

Combine like terms: 45 + -45 = 0
-54 + 5x + 11x2 = 0 + 15x + -15x + -10x2 + 10x2
-54 + 5x + 11x2 = 15x + -15x + -10x2 + 10x2

Combine like terms: 15x + -15x = 0
-54 + 5x + 11x2 = 0 + -10x2 + 10x2
-54 + 5x + 11x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
-54 + 5x + 11x2 = 0

Factor a trinomial.
(-27 + -11x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-27 + -11x)' equal to zero and attempt to solve: Simplifying -27 + -11x = 0 Solving -27 + -11x = 0 Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + -11x = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -11x = 0 + 27 -11x = 0 + 27 Combine like terms: 0 + 27 = 27 -11x = 27 Divide each side by '-11'. x = -2.454545455 Simplifying x = -2.454545455

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-2.454545455, 2}

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