x*x=4(x-3)*(x-3)

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Solution for x*x=4(x-3)*(x-3) equation:


Simplifying
x * x = 4(x + -3)(x + -3)

Multiply x * x
x2 = 4(x + -3)(x + -3)

Reorder the terms:
x2 = 4(-3 + x)(x + -3)

Reorder the terms:
x2 = 4(-3 + x)(-3 + x)

Multiply (-3 + x) * (-3 + x)
x2 = 4(-3(-3 + x) + x(-3 + x))
x2 = 4((-3 * -3 + x * -3) + x(-3 + x))
x2 = 4((9 + -3x) + x(-3 + x))
x2 = 4(9 + -3x + (-3 * x + x * x))
x2 = 4(9 + -3x + (-3x + x2))

Combine like terms: -3x + -3x = -6x
x2 = 4(9 + -6x + x2)
x2 = (9 * 4 + -6x * 4 + x2 * 4)
x2 = (36 + -24x + 4x2)

Solving
x2 = 36 + -24x + 4x2

Solving for variable 'x'.

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

Combine like terms: x2 + -4x2 = -3x2
-36 + 24x + -3x2 = 36 + -24x + 4x2 + -36 + 24x + -4x2

Reorder the terms:
-36 + 24x + -3x2 = 36 + -36 + -24x + 24x + 4x2 + -4x2

Combine like terms: 36 + -36 = 0
-36 + 24x + -3x2 = 0 + -24x + 24x + 4x2 + -4x2
-36 + 24x + -3x2 = -24x + 24x + 4x2 + -4x2

Combine like terms: -24x + 24x = 0
-36 + 24x + -3x2 = 0 + 4x2 + -4x2
-36 + 24x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-36 + 24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 8x + -1x2) = 0

Factor a trinomial.
3((-6 + x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {6, 2}

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