(-2x+1)(x+4)+2(2x-1)(x+1)=0

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Solution for (-2x+1)(x+4)+2(2x-1)(x+1)=0 equation:


Simplifying
(-2x + 1)(x + 4) + 2(2x + -1)(x + 1) = 0

Reorder the terms:
(1 + -2x)(x + 4) + 2(2x + -1)(x + 1) = 0

Reorder the terms:
(1 + -2x)(4 + x) + 2(2x + -1)(x + 1) = 0

Multiply (1 + -2x) * (4 + x)
(1(4 + x) + -2x * (4 + x)) + 2(2x + -1)(x + 1) = 0
((4 * 1 + x * 1) + -2x * (4 + x)) + 2(2x + -1)(x + 1) = 0
((4 + 1x) + -2x * (4 + x)) + 2(2x + -1)(x + 1) = 0
(4 + 1x + (4 * -2x + x * -2x)) + 2(2x + -1)(x + 1) = 0
(4 + 1x + (-8x + -2x2)) + 2(2x + -1)(x + 1) = 0

Combine like terms: 1x + -8x = -7x
(4 + -7x + -2x2) + 2(2x + -1)(x + 1) = 0

Reorder the terms:
4 + -7x + -2x2 + 2(-1 + 2x)(x + 1) = 0

Reorder the terms:
4 + -7x + -2x2 + 2(-1 + 2x)(1 + x) = 0

Multiply (-1 + 2x) * (1 + x)
4 + -7x + -2x2 + 2(-1(1 + x) + 2x * (1 + x)) = 0
4 + -7x + -2x2 + 2((1 * -1 + x * -1) + 2x * (1 + x)) = 0
4 + -7x + -2x2 + 2((-1 + -1x) + 2x * (1 + x)) = 0
4 + -7x + -2x2 + 2(-1 + -1x + (1 * 2x + x * 2x)) = 0
4 + -7x + -2x2 + 2(-1 + -1x + (2x + 2x2)) = 0

Combine like terms: -1x + 2x = 1x
4 + -7x + -2x2 + 2(-1 + 1x + 2x2) = 0
4 + -7x + -2x2 + (-1 * 2 + 1x * 2 + 2x2 * 2) = 0
4 + -7x + -2x2 + (-2 + 2x + 4x2) = 0

Reorder the terms:
4 + -2 + -7x + 2x + -2x2 + 4x2 = 0

Combine like terms: 4 + -2 = 2
2 + -7x + 2x + -2x2 + 4x2 = 0

Combine like terms: -7x + 2x = -5x
2 + -5x + -2x2 + 4x2 = 0

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

Solving
2 + -5x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

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 = {0.5, 2}

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