(X-5)(2X+1)=3X-15

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Solution for (X-5)(2X+1)=3X-15 equation: 


Simplifying
(X + -5)(2X + 1) = 3X + -15

Reorder the terms:
(-5 + X)(2X + 1) = 3X + -15

Reorder the terms:
(-5 + X)(1 + 2X) = 3X + -15

Multiply (-5 + X) * (1 + 2X)
(-5(1 + 2X) + X(1 + 2X)) = 3X + -15
((1 * -5 + 2X * -5) + X(1 + 2X)) = 3X + -15
((-5 + -10X) + X(1 + 2X)) = 3X + -15
(-5 + -10X + (1 * X + 2X * X)) = 3X + -15
(-5 + -10X + (1X + 2X2)) = 3X + -15

Combine like terms: -10X + 1X = -9X
(-5 + -9X + 2X2) = 3X + -15

Reorder the terms:
-5 + -9X + 2X2 = -15 + 3X

Solving
-5 + -9X + 2X2 = -15 + 3X

Solving for variable 'X'.

Reorder the terms:
-5 + 15 + -9X + -3X + 2X2 = -15 + 3X + 15 + -3X

Combine like terms: -5 + 15 = 10
10 + -9X + -3X + 2X2 = -15 + 3X + 15 + -3X

Combine like terms: -9X + -3X = -12X
10 + -12X + 2X2 = -15 + 3X + 15 + -3X

Reorder the terms:
10 + -12X + 2X2 = -15 + 15 + 3X + -3X

Combine like terms: -15 + 15 = 0
10 + -12X + 2X2 = 0 + 3X + -3X
10 + -12X + 2X2 = 3X + -3X

Combine like terms: 3X + -3X = 0
10 + -12X + 2X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -6X + X2) = 0

Factor a trinomial.
2((1 + -1X)(5 + -1X)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1X = 0 + -1

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

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

Divide each side by '-1'.
X = 1

Simplifying
X = 1

Subproblem 2
Set the factor '(5 + -1X)' equal to zero and attempt to solve:

Simplifying
5 + -1X = 0

Solving
5 + -1X = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1X = 0 + -5
-1X = 0 + -5

Combine like terms: 0 + -5 = -5
-1X = -5

Divide each side by '-1'.
X = 5

Simplifying
X = 5
Solution
X = {1, 5}

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