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

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


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

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

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

Multiply (-7 + 2x) * (3 + x)
(-7(3 + x) + 2x * (3 + x)) = 2x + -7
((3 * -7 + x * -7) + 2x * (3 + x)) = 2x + -7
((-21 + -7x) + 2x * (3 + x)) = 2x + -7
(-21 + -7x + (3 * 2x + x * 2x)) = 2x + -7
(-21 + -7x + (6x + 2x2)) = 2x + -7

Combine like terms: -7x + 6x = -1x
(-21 + -1x + 2x2) = 2x + -7

Reorder the terms:
-21 + -1x + 2x2 = -7 + 2x

Solving
-21 + -1x + 2x2 = -7 + 2x

Solving for variable 'x'.

Reorder the terms:
-21 + 7 + -1x + -2x + 2x2 = -7 + 2x + 7 + -2x

Combine like terms: -21 + 7 = -14
-14 + -1x + -2x + 2x2 = -7 + 2x + 7 + -2x

Combine like terms: -1x + -2x = -3x
-14 + -3x + 2x2 = -7 + 2x + 7 + -2x

Reorder the terms:
-14 + -3x + 2x2 = -7 + 7 + 2x + -2x

Combine like terms: -7 + 7 = 0
-14 + -3x + 2x2 = 0 + 2x + -2x
-14 + -3x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-14 + -3x + 2x2 = 0

Factor a trinomial.
(-2 + -1x)(7 + -2x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-2, 3.5}

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