(x+5)(x-6)=(2x+3)(x-6)

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Solution for (x+5)(x-6)=(2x+3)(x-6) equation:


Simplifying
(x + 5)(x + -6) = (2x + 3)(x + -6)

Reorder the terms:
(5 + x)(x + -6) = (2x + 3)(x + -6)

Reorder the terms:
(5 + x)(-6 + x) = (2x + 3)(x + -6)

Multiply (5 + x) * (-6 + x)
(5(-6 + x) + x(-6 + x)) = (2x + 3)(x + -6)
((-6 * 5 + x * 5) + x(-6 + x)) = (2x + 3)(x + -6)
((-30 + 5x) + x(-6 + x)) = (2x + 3)(x + -6)
(-30 + 5x + (-6 * x + x * x)) = (2x + 3)(x + -6)
(-30 + 5x + (-6x + x2)) = (2x + 3)(x + -6)

Combine like terms: 5x + -6x = -1x
(-30 + -1x + x2) = (2x + 3)(x + -6)

Reorder the terms:
-30 + -1x + x2 = (3 + 2x)(x + -6)

Reorder the terms:
-30 + -1x + x2 = (3 + 2x)(-6 + x)

Multiply (3 + 2x) * (-6 + x)
-30 + -1x + x2 = (3(-6 + x) + 2x * (-6 + x))
-30 + -1x + x2 = ((-6 * 3 + x * 3) + 2x * (-6 + x))
-30 + -1x + x2 = ((-18 + 3x) + 2x * (-6 + x))
-30 + -1x + x2 = (-18 + 3x + (-6 * 2x + x * 2x))
-30 + -1x + x2 = (-18 + 3x + (-12x + 2x2))

Combine like terms: 3x + -12x = -9x
-30 + -1x + x2 = (-18 + -9x + 2x2)

Solving
-30 + -1x + x2 = -18 + -9x + 2x2

Solving for variable 'x'.

Reorder the terms:
-30 + 18 + -1x + 9x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2

Combine like terms: -30 + 18 = -12
-12 + -1x + 9x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2

Combine like terms: -1x + 9x = 8x
-12 + 8x + x2 + -2x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-12 + 8x + -1x2 = -18 + -9x + 2x2 + 18 + 9x + -2x2

Reorder the terms:
-12 + 8x + -1x2 = -18 + 18 + -9x + 9x + 2x2 + -2x2

Combine like terms: -18 + 18 = 0
-12 + 8x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2
-12 + 8x + -1x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
-12 + 8x + -1x2 = 0 + 2x2 + -2x2
-12 + 8x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + 8x + -1x2 = 0

Factor a trinomial.
(-6 + x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6

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 = {6, 2}

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