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

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


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

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

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

Multiply (-1 + 2x) * (2 + x)
(-1(2 + x) + 2x * (2 + x)) = 7
((2 * -1 + x * -1) + 2x * (2 + x)) = 7
((-2 + -1x) + 2x * (2 + x)) = 7
(-2 + -1x + (2 * 2x + x * 2x)) = 7
(-2 + -1x + (4x + 2x2)) = 7

Combine like terms: -1x + 4x = 3x
(-2 + 3x + 2x2) = 7

Solving
-2 + 3x + 2x2 = 7

Solving for variable 'x'.

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

Combine like terms: -2 + -7 = -9
-9 + 3x + 2x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-9 + 3x + 2x2 = 0

Factor a trinomial.
(-3 + -1x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-3, 1.5}

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