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

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


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

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

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

Multiply (-1 + 2x) * (2 + x)
(-1(2 + x) + 2x * (2 + x)) = -3
((2 * -1 + x * -1) + 2x * (2 + x)) = -3
((-2 + -1x) + 2x * (2 + x)) = -3
(-2 + -1x + (2 * 2x + x * 2x)) = -3
(-2 + -1x + (4x + 2x2)) = -3

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

Solving
-2 + 3x + 2x2 = -3

Solving for variable 'x'.

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

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

Combine like terms: -3 + 3 = 0
1 + 3x + 2x2 = 0

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

Subproblem 1

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

Subproblem 2

Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5

Solution

x = {-1, -0.5}

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