(2x+3)(x-1)=-4x

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Solution for (2x+3)(x-1)=-4x equation:


Simplifying
(2x + 3)(x + -1) = -4x

Reorder the terms:
(3 + 2x)(x + -1) = -4x

Reorder the terms:
(3 + 2x)(-1 + x) = -4x

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

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

Solving
-3 + 1x + 2x2 = -4x

Solving for variable 'x'.

Reorder the terms:
-3 + 1x + 4x + 2x2 = -4x + 4x

Combine like terms: 1x + 4x = 5x
-3 + 5x + 2x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-3 + 5x + 2x2 = 0

Factor a trinomial.
(-3 + -1x)(1 + -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 '(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 = {-3, 0.5}

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