4x^2-24x+36=12x-36

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Solution for 4x^2-24x+36=12x-36 equation:


Simplifying
4x2 + -24x + 36 = 12x + -36

Reorder the terms:
36 + -24x + 4x2 = 12x + -36

Reorder the terms:
36 + -24x + 4x2 = -36 + 12x

Solving
36 + -24x + 4x2 = -36 + 12x

Solving for variable 'x'.

Reorder the terms:
36 + 36 + -24x + -12x + 4x2 = -36 + 12x + 36 + -12x

Combine like terms: 36 + 36 = 72
72 + -24x + -12x + 4x2 = -36 + 12x + 36 + -12x

Combine like terms: -24x + -12x = -36x
72 + -36x + 4x2 = -36 + 12x + 36 + -12x

Reorder the terms:
72 + -36x + 4x2 = -36 + 36 + 12x + -12x

Combine like terms: -36 + 36 = 0
72 + -36x + 4x2 = 0 + 12x + -12x
72 + -36x + 4x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
72 + -36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -9x + x2) = 0

Factor a trinomial.
4((3 + -1x)(6 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {3, 6}

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