7x^2-13x=5x^2-8x

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Solution for 7x^2-13x=5x^2-8x equation:


Simplifying
7x2 + -13x = 5x2 + -8x

Reorder the terms:
-13x + 7x2 = 5x2 + -8x

Reorder the terms:
-13x + 7x2 = -8x + 5x2

Solving
-13x + 7x2 = -8x + 5x2

Solving for variable 'x'.

Reorder the terms:
-13x + 8x + 7x2 + -5x2 = -8x + 5x2 + 8x + -5x2

Combine like terms: -13x + 8x = -5x
-5x + 7x2 + -5x2 = -8x + 5x2 + 8x + -5x2

Combine like terms: 7x2 + -5x2 = 2x2
-5x + 2x2 = -8x + 5x2 + 8x + -5x2

Reorder the terms:
-5x + 2x2 = -8x + 8x + 5x2 + -5x2

Combine like terms: -8x + 8x = 0
-5x + 2x2 = 0 + 5x2 + -5x2
-5x + 2x2 = 5x2 + -5x2

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 2x) = 0

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 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 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 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Divide each side by '2'. x = 2.5 Simplifying x = 2.5

Solution

x = {0, 2.5}

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