7x^2-3x=11x^2+5x

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Solution for 7x^2-3x=11x^2+5x equation:


Simplifying
7x2 + -3x = 11x2 + 5x

Reorder the terms:
-3x + 7x2 = 11x2 + 5x

Reorder the terms:
-3x + 7x2 = 5x + 11x2

Solving
-3x + 7x2 = 5x + 11x2

Solving for variable 'x'.

Reorder the terms:
-3x + -5x + 7x2 + -11x2 = 5x + 11x2 + -5x + -11x2

Combine like terms: -3x + -5x = -8x
-8x + 7x2 + -11x2 = 5x + 11x2 + -5x + -11x2

Combine like terms: 7x2 + -11x2 = -4x2
-8x + -4x2 = 5x + 11x2 + -5x + -11x2

Reorder the terms:
-8x + -4x2 = 5x + -5x + 11x2 + -11x2

Combine like terms: 5x + -5x = 0
-8x + -4x2 = 0 + 11x2 + -11x2
-8x + -4x2 = 11x2 + -11x2

Combine like terms: 11x2 + -11x2 = 0
-8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-4x'.
-4x(2 + 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {0, -2}

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