29x^2-10x+1=25x^2+10x+1

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Solution for 29x^2-10x+1=25x^2+10x+1 equation:


Simplifying
29x2 + -10x + 1 = 25x2 + 10x + 1

Reorder the terms:
1 + -10x + 29x2 = 25x2 + 10x + 1

Reorder the terms:
1 + -10x + 29x2 = 1 + 10x + 25x2

Add '-1' to each side of the equation.
1 + -10x + -1 + 29x2 = 1 + 10x + -1 + 25x2

Reorder the terms:
1 + -1 + -10x + 29x2 = 1 + 10x + -1 + 25x2

Combine like terms: 1 + -1 = 0
0 + -10x + 29x2 = 1 + 10x + -1 + 25x2
-10x + 29x2 = 1 + 10x + -1 + 25x2

Reorder the terms:
-10x + 29x2 = 1 + -1 + 10x + 25x2

Combine like terms: 1 + -1 = 0
-10x + 29x2 = 0 + 10x + 25x2
-10x + 29x2 = 10x + 25x2

Solving
-10x + 29x2 = 10x + 25x2

Solving for variable 'x'.

Reorder the terms:
-10x + -10x + 29x2 + -25x2 = 10x + 25x2 + -10x + -25x2

Combine like terms: -10x + -10x = -20x
-20x + 29x2 + -25x2 = 10x + 25x2 + -10x + -25x2

Combine like terms: 29x2 + -25x2 = 4x2
-20x + 4x2 = 10x + 25x2 + -10x + -25x2

Reorder the terms:
-20x + 4x2 = 10x + -10x + 25x2 + -25x2

Combine like terms: 10x + -10x = 0
-20x + 4x2 = 0 + 25x2 + -25x2
-20x + 4x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
-20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-5 + x) = 0

Ignore the factor 4.

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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5

Solution

x = {0, 5}

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