(X+2)(X-1)=7X+5

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Solution for (X+2)(X-1)=7X+5 equation: 


Simplifying
(X + 2)(X + -1) = 7X + 5

Reorder the terms:
(2 + X)(X + -1) = 7X + 5

Reorder the terms:
(2 + X)(-1 + X) = 7X + 5

Multiply (2 + X) * (-1 + X)
(2(-1 + X) + X(-1 + X)) = 7X + 5
((-1 * 2 + X * 2) + X(-1 + X)) = 7X + 5
((-2 + 2X) + X(-1 + X)) = 7X + 5
(-2 + 2X + (-1 * X + X * X)) = 7X + 5
(-2 + 2X + (-1X + X2)) = 7X + 5

Combine like terms: 2X + -1X = 1X
(-2 + 1X + X2) = 7X + 5

Reorder the terms:
-2 + 1X + X2 = 5 + 7X

Solving
-2 + 1X + X2 = 5 + 7X

Solving for variable 'X'.

Reorder the terms:
-2 + -5 + 1X + -7X + X2 = 5 + 7X + -5 + -7X

Combine like terms: -2 + -5 = -7
-7 + 1X + -7X + X2 = 5 + 7X + -5 + -7X

Combine like terms: 1X + -7X = -6X
-7 + -6X + X2 = 5 + 7X + -5 + -7X

Reorder the terms:
-7 + -6X + X2 = 5 + -5 + 7X + -7X

Combine like terms: 5 + -5 = 0
-7 + -6X + X2 = 0 + 7X + -7X
-7 + -6X + X2 = 7X + -7X

Combine like terms: 7X + -7X = 0
-7 + -6X + X2 = 0

Factor a trinomial.
(-1 + -1X)(7 + -1X) = 0


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 '(7 + -1X)' equal to zero and attempt to solve:

Simplifying
7 + -1X = 0

Solving
7 + -1X = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1X = 0 + -7

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

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

Divide each side by '-1'.
X = 7

Simplifying
X = 7
Solution
X = {-1, 7}

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