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

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Solution for (15-x)(x-2)=(x-6)(x+5) equation:


Simplifying
(15 + -1x)(x + -2) = (x + -6)(x + 5)

Reorder the terms:
(15 + -1x)(-2 + x) = (x + -6)(x + 5)

Multiply (15 + -1x) * (-2 + x)
(15(-2 + x) + -1x * (-2 + x)) = (x + -6)(x + 5)
((-2 * 15 + x * 15) + -1x * (-2 + x)) = (x + -6)(x + 5)
((-30 + 15x) + -1x * (-2 + x)) = (x + -6)(x + 5)
(-30 + 15x + (-2 * -1x + x * -1x)) = (x + -6)(x + 5)
(-30 + 15x + (2x + -1x2)) = (x + -6)(x + 5)

Combine like terms: 15x + 2x = 17x
(-30 + 17x + -1x2) = (x + -6)(x + 5)

Reorder the terms:
-30 + 17x + -1x2 = (-6 + x)(x + 5)

Reorder the terms:
-30 + 17x + -1x2 = (-6 + x)(5 + x)

Multiply (-6 + x) * (5 + x)
-30 + 17x + -1x2 = (-6(5 + x) + x(5 + x))
-30 + 17x + -1x2 = ((5 * -6 + x * -6) + x(5 + x))
-30 + 17x + -1x2 = ((-30 + -6x) + x(5 + x))
-30 + 17x + -1x2 = (-30 + -6x + (5 * x + x * x))
-30 + 17x + -1x2 = (-30 + -6x + (5x + x2))

Combine like terms: -6x + 5x = -1x
-30 + 17x + -1x2 = (-30 + -1x + x2)

Add '30' to each side of the equation.
-30 + 17x + 30 + -1x2 = -30 + -1x + 30 + x2

Reorder the terms:
-30 + 30 + 17x + -1x2 = -30 + -1x + 30 + x2

Combine like terms: -30 + 30 = 0
0 + 17x + -1x2 = -30 + -1x + 30 + x2
17x + -1x2 = -30 + -1x + 30 + x2

Reorder the terms:
17x + -1x2 = -30 + 30 + -1x + x2

Combine like terms: -30 + 30 = 0
17x + -1x2 = 0 + -1x + x2
17x + -1x2 = -1x + x2

Solving
17x + -1x2 = -1x + x2

Solving for variable 'x'.

Reorder the terms:
17x + x + -1x2 + -1x2 = -1x + x2 + x + -1x2

Combine like terms: 17x + x = 18x
18x + -1x2 + -1x2 = -1x + x2 + x + -1x2

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2x'.
2x(9 + -1x) = 0

Ignore the factor 2.

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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9

Solution

x = {0, 9}

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