58-12x+3x^2=58-6x+x^2

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Solution for 58-12x+3x^2=58-6x+x^2 equation:


Simplifying
58 + -12x + 3x2 = 58 + -6x + x2

Add '-58' to each side of the equation.
58 + -12x + -58 + 3x2 = 58 + -6x + -58 + x2

Reorder the terms:
58 + -58 + -12x + 3x2 = 58 + -6x + -58 + x2

Combine like terms: 58 + -58 = 0
0 + -12x + 3x2 = 58 + -6x + -58 + x2
-12x + 3x2 = 58 + -6x + -58 + x2

Reorder the terms:
-12x + 3x2 = 58 + -58 + -6x + x2

Combine like terms: 58 + -58 = 0
-12x + 3x2 = 0 + -6x + x2
-12x + 3x2 = -6x + x2

Solving
-12x + 3x2 = -6x + x2

Solving for variable 'x'.

Reorder the terms:
-12x + 6x + 3x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: -12x + 6x = -6x
-6x + 3x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-6x + 2x2 = -6x + x2 + 6x + -1x2

Reorder the terms:
-6x + 2x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-6x + 2x2 = 0 + x2 + -1x2
-6x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6x + 2x2 = 0

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

Ignore the factor 2.

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 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3

Solution

x = {0, 3}

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