(2x+5)(1-x)=5

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Solution for (2x+5)(1-x)=5 equation:


Simplifying
(2x + 5)(1 + -1x) = 5

Reorder the terms:
(5 + 2x)(1 + -1x) = 5

Multiply (5 + 2x) * (1 + -1x)
(5(1 + -1x) + 2x * (1 + -1x)) = 5
((1 * 5 + -1x * 5) + 2x * (1 + -1x)) = 5
((5 + -5x) + 2x * (1 + -1x)) = 5
(5 + -5x + (1 * 2x + -1x * 2x)) = 5
(5 + -5x + (2x + -2x2)) = 5

Combine like terms: -5x + 2x = -3x
(5 + -3x + -2x2) = 5

Add '-5' to each side of the equation.
5 + -3x + -5 + -2x2 = 5 + -5

Reorder the terms:
5 + -5 + -3x + -2x2 = 5 + -5

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

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

Solving
-3x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(3 + 2x) = 0

Ignore the factor -1.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

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 = {0, -1.5}

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