5(x+3)-5(x^2-1)=x^2+7(3-x)-1

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Solution for 5(x+3)-5(x^2-1)=x^2+7(3-x)-1 equation:


Simplifying
5(x + 3) + -5(x2 + -1) = x2 + 7(3 + -1x) + -1

Reorder the terms:
5(3 + x) + -5(x2 + -1) = x2 + 7(3 + -1x) + -1
(3 * 5 + x * 5) + -5(x2 + -1) = x2 + 7(3 + -1x) + -1
(15 + 5x) + -5(x2 + -1) = x2 + 7(3 + -1x) + -1

Reorder the terms:
15 + 5x + -5(-1 + x2) = x2 + 7(3 + -1x) + -1
15 + 5x + (-1 * -5 + x2 * -5) = x2 + 7(3 + -1x) + -1
15 + 5x + (5 + -5x2) = x2 + 7(3 + -1x) + -1

Reorder the terms:
15 + 5 + 5x + -5x2 = x2 + 7(3 + -1x) + -1

Combine like terms: 15 + 5 = 20
20 + 5x + -5x2 = x2 + 7(3 + -1x) + -1
20 + 5x + -5x2 = x2 + (3 * 7 + -1x * 7) + -1
20 + 5x + -5x2 = x2 + (21 + -7x) + -1

Reorder the terms:
20 + 5x + -5x2 = 21 + -1 + -7x + x2

Combine like terms: 21 + -1 = 20
20 + 5x + -5x2 = 20 + -7x + x2

Add '-20' to each side of the equation.
20 + 5x + -20 + -5x2 = 20 + -7x + -20 + x2

Reorder the terms:
20 + -20 + 5x + -5x2 = 20 + -7x + -20 + x2

Combine like terms: 20 + -20 = 0
0 + 5x + -5x2 = 20 + -7x + -20 + x2
5x + -5x2 = 20 + -7x + -20 + x2

Reorder the terms:
5x + -5x2 = 20 + -20 + -7x + x2

Combine like terms: 20 + -20 = 0
5x + -5x2 = 0 + -7x + x2
5x + -5x2 = -7x + x2

Solving
5x + -5x2 = -7x + x2

Solving for variable 'x'.

Reorder the terms:
5x + 7x + -5x2 + -1x2 = -7x + x2 + 7x + -1x2

Combine like terms: 5x + 7x = 12x
12x + -5x2 + -1x2 = -7x + x2 + 7x + -1x2

Combine like terms: -5x2 + -1x2 = -6x2
12x + -6x2 = -7x + x2 + 7x + -1x2

Reorder the terms:
12x + -6x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
12x + -6x2 = 0 + x2 + -1x2
12x + -6x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(2 + -1x) = 0

Ignore the factor 6.

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 '(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, 2}

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