(2x-1)(x+7)=3(x-5)

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Solution for (2x-1)(x+7)=3(x-5) equation: 


Simplifying
(2x + -1)(x + 7) = 3(x + -5)

Reorder the terms:
(-1 + 2x)(x + 7) = 3(x + -5)

Reorder the terms:
(-1 + 2x)(7 + x) = 3(x + -5)

Multiply (-1 + 2x) * (7 + x)
(-1(7 + x) + 2x * (7 + x)) = 3(x + -5)
((7 * -1 + x * -1) + 2x * (7 + x)) = 3(x + -5)
((-7 + -1x) + 2x * (7 + x)) = 3(x + -5)
(-7 + -1x + (7 * 2x + x * 2x)) = 3(x + -5)
(-7 + -1x + (14x + 2x2)) = 3(x + -5)

Combine like terms: -1x + 14x = 13x
(-7 + 13x + 2x2) = 3(x + -5)

Reorder the terms:
-7 + 13x + 2x2 = 3(-5 + x)
-7 + 13x + 2x2 = (-5 * 3 + x * 3)
-7 + 13x + 2x2 = (-15 + 3x)

Solving
-7 + 13x + 2x2 = -15 + 3x

Solving for variable 'x'.

Reorder the terms:
-7 + 15 + 13x + -3x + 2x2 = -15 + 3x + 15 + -3x

Combine like terms: -7 + 15 = 8
8 + 13x + -3x + 2x2 = -15 + 3x + 15 + -3x

Combine like terms: 13x + -3x = 10x
8 + 10x + 2x2 = -15 + 3x + 15 + -3x

Reorder the terms:
8 + 10x + 2x2 = -15 + 15 + 3x + -3x

Combine like terms: -15 + 15 = 0
8 + 10x + 2x2 = 0 + 3x + -3x
8 + 10x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
8 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 5x + x2) = 0

Factor a trinomial.
2((4 + x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-4, -1}

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