(X-6)(2X+5)=(X+10)(X-3)

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Solution for (X-6)(2X+5)=(X+10)(X-3) equation: 


Simplifying
(X + -6)(2X + 5) = (X + 10)(X + -3)

Reorder the terms:
(-6 + X)(2X + 5) = (X + 10)(X + -3)

Reorder the terms:
(-6 + X)(5 + 2X) = (X + 10)(X + -3)

Multiply (-6 + X) * (5 + 2X)
(-6(5 + 2X) + X(5 + 2X)) = (X + 10)(X + -3)
((5 * -6 + 2X * -6) + X(5 + 2X)) = (X + 10)(X + -3)
((-30 + -12X) + X(5 + 2X)) = (X + 10)(X + -3)
(-30 + -12X + (5 * X + 2X * X)) = (X + 10)(X + -3)
(-30 + -12X + (5X + 2X2)) = (X + 10)(X + -3)

Combine like terms: -12X + 5X = -7X
(-30 + -7X + 2X2) = (X + 10)(X + -3)

Reorder the terms:
-30 + -7X + 2X2 = (10 + X)(X + -3)

Reorder the terms:
-30 + -7X + 2X2 = (10 + X)(-3 + X)

Multiply (10 + X) * (-3 + X)
-30 + -7X + 2X2 = (10(-3 + X) + X(-3 + X))
-30 + -7X + 2X2 = ((-3 * 10 + X * 10) + X(-3 + X))
-30 + -7X + 2X2 = ((-30 + 10X) + X(-3 + X))
-30 + -7X + 2X2 = (-30 + 10X + (-3 * X + X * X))
-30 + -7X + 2X2 = (-30 + 10X + (-3X + X2))

Combine like terms: 10X + -3X = 7X
-30 + -7X + 2X2 = (-30 + 7X + X2)

Add '30' to each side of the equation.
-30 + -7X + 30 + 2X2 = -30 + 7X + 30 + X2

Reorder the terms:
-30 + 30 + -7X + 2X2 = -30 + 7X + 30 + X2

Combine like terms: -30 + 30 = 0
0 + -7X + 2X2 = -30 + 7X + 30 + X2
-7X + 2X2 = -30 + 7X + 30 + X2

Reorder the terms:
-7X + 2X2 = -30 + 30 + 7X + X2

Combine like terms: -30 + 30 = 0
-7X + 2X2 = 0 + 7X + X2
-7X + 2X2 = 7X + X2

Solving
-7X + 2X2 = 7X + X2

Solving for variable 'X'.

Reorder the terms:
-7X + -7X + 2X2 + -1X2 = 7X + X2 + -7X + -1X2

Combine like terms: -7X + -7X = -14X
-14X + 2X2 + -1X2 = 7X + X2 + -7X + -1X2

Combine like terms: 2X2 + -1X2 = 1X2
-14X + 1X2 = 7X + X2 + -7X + -1X2

Reorder the terms:
-14X + 1X2 = 7X + -7X + X2 + -1X2

Combine like terms: 7X + -7X = 0
-14X + 1X2 = 0 + X2 + -1X2
-14X + 1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-14X + 1X2 = 0

Factor out the Greatest Common Factor (GCF), 'X'.
X(-14 + 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 '(-14 + X)' equal to zero and attempt to solve:

Simplifying
-14 + X = 0

Solving
-14 + X = 0

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

Add '14' to each side of the equation.
-14 + 14 + X = 0 + 14

Combine like terms: -14 + 14 = 0
0 + X = 0 + 14
X = 0 + 14

Combine like terms: 0 + 14 = 14
X = 14

Simplifying
X = 14
Solution
X = {0, 14}

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