(x-6)(2x+3)=(x+9)(x-2)

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Solution for (x-6)(2x+3)=(x+9)(x-2) equation:


Simplifying
(x + -6)(2x + 3) = (x + 9)(x + -2)

Reorder the terms:
(-6 + x)(2x + 3) = (x + 9)(x + -2)

Reorder the terms:
(-6 + x)(3 + 2x) = (x + 9)(x + -2)

Multiply (-6 + x) * (3 + 2x)
(-6(3 + 2x) + x(3 + 2x)) = (x + 9)(x + -2)
((3 * -6 + 2x * -6) + x(3 + 2x)) = (x + 9)(x + -2)
((-18 + -12x) + x(3 + 2x)) = (x + 9)(x + -2)
(-18 + -12x + (3 * x + 2x * x)) = (x + 9)(x + -2)
(-18 + -12x + (3x + 2x2)) = (x + 9)(x + -2)

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

Reorder the terms:
-18 + -9x + 2x2 = (9 + x)(x + -2)

Reorder the terms:
-18 + -9x + 2x2 = (9 + x)(-2 + x)

Multiply (9 + x) * (-2 + x)
-18 + -9x + 2x2 = (9(-2 + x) + x(-2 + x))
-18 + -9x + 2x2 = ((-2 * 9 + x * 9) + x(-2 + x))
-18 + -9x + 2x2 = ((-18 + 9x) + x(-2 + x))
-18 + -9x + 2x2 = (-18 + 9x + (-2 * x + x * x))
-18 + -9x + 2x2 = (-18 + 9x + (-2x + x2))

Combine like terms: 9x + -2x = 7x
-18 + -9x + 2x2 = (-18 + 7x + x2)

Add '18' to each side of the equation.
-18 + -9x + 18 + 2x2 = -18 + 7x + 18 + x2

Reorder the terms:
-18 + 18 + -9x + 2x2 = -18 + 7x + 18 + x2

Combine like terms: -18 + 18 = 0
0 + -9x + 2x2 = -18 + 7x + 18 + x2
-9x + 2x2 = -18 + 7x + 18 + x2

Reorder the terms:
-9x + 2x2 = -18 + 18 + 7x + x2

Combine like terms: -18 + 18 = 0
-9x + 2x2 = 0 + 7x + x2
-9x + 2x2 = 7x + x2

Solving
-9x + 2x2 = 7x + x2

Solving for variable 'x'.

Reorder the terms:
-9x + -7x + 2x2 + -1x2 = 7x + x2 + -7x + -1x2

Combine like terms: -9x + -7x = -16x
-16x + 2x2 + -1x2 = 7x + x2 + -7x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-16x + 1x2 = 7x + x2 + -7x + -1x2

Reorder the terms:
-16x + 1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-16x + 1x2 = 0 + x2 + -1x2
-16x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-16x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-16 + x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(-16 + x)' equal to zero and attempt to solve: Simplifying -16 + x = 0 Solving -16 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + x = 0 + 16 x = 0 + 16 Combine like terms: 0 + 16 = 16 x = 16 Simplifying x = 16

Solution

x = {0, 16}

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