x(45+34)=x(x-3)

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Solution for x(45+34)=x(x-3) equation:


Simplifying
x(45 + 34) = x(x + -3)

Combine like terms: 45 + 34 = 79
x(79) = x(x + -3)

Reorder the terms for easier multiplication:
79x = x(x + -3)

Reorder the terms:
79x = x(-3 + x)
79x = (-3 * x + x * x)
79x = (-3x + x2)

Solving
79x = -3x + x2

Solving for variable 'x'.

Combine like terms: 79x + 3x = 82x
82x + -1x2 = -3x + x2 + 3x + -1x2

Reorder the terms:
82x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
82x + -1x2 = 0 + x2 + -1x2
82x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
82x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(82 + -1x) = 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 '(82 + -1x)' equal to zero and attempt to solve: Simplifying 82 + -1x = 0 Solving 82 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-82' to each side of the equation. 82 + -82 + -1x = 0 + -82 Combine like terms: 82 + -82 = 0 0 + -1x = 0 + -82 -1x = 0 + -82 Combine like terms: 0 + -82 = -82 -1x = -82 Divide each side by '-1'. x = 82 Simplifying x = 82

Solution

x = {0, 82}

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