x^2-6x+9+4x^2-24x+36=0

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Solution for x^2-6x+9+4x^2-24x+36=0 equation:


Simplifying
x2 + -6x + 9 + 4x2 + -24x + 36 = 0

Reorder the terms:
9 + 36 + -6x + -24x + x2 + 4x2 = 0

Combine like terms: 9 + 36 = 45
45 + -6x + -24x + x2 + 4x2 = 0

Combine like terms: -6x + -24x = -30x
45 + -30x + x2 + 4x2 = 0

Combine like terms: x2 + 4x2 = 5x2
45 + -30x + 5x2 = 0

Solving
45 + -30x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(9 + -6x + x2) = 0

Factor a trinomial.
5((3 + -1x)(3 + -1x)) = 0

Ignore the factor 5.

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 '(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

Solution

x = {3, 3}

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