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

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


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

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

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

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

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

Solving
-3 + 1x + 2x2 = 7

Solving for variable 'x'.

Reorder the terms:
-3 + -7 + 1x + 2x2 = 7 + -7

Combine like terms: -3 + -7 = -10
-10 + 1x + 2x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-10 + 1x + 2x2 = 0

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


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

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
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
Solution
x = {-2.5, 2}

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