4(x-4)(x-4)=3(x-6)(x+2)

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Solution for 4(x-4)(x-4)=3(x-6)(x+2) equation:


Simplifying
4(x + -4)(x + -4) = 3(x + -6)(x + 2)

Reorder the terms:
4(-4 + x)(x + -4) = 3(x + -6)(x + 2)

Reorder the terms:
4(-4 + x)(-4 + x) = 3(x + -6)(x + 2)

Multiply (-4 + x) * (-4 + x)
4(-4(-4 + x) + x(-4 + x)) = 3(x + -6)(x + 2)
4((-4 * -4 + x * -4) + x(-4 + x)) = 3(x + -6)(x + 2)
4((16 + -4x) + x(-4 + x)) = 3(x + -6)(x + 2)
4(16 + -4x + (-4 * x + x * x)) = 3(x + -6)(x + 2)
4(16 + -4x + (-4x + x2)) = 3(x + -6)(x + 2)

Combine like terms: -4x + -4x = -8x
4(16 + -8x + x2) = 3(x + -6)(x + 2)
(16 * 4 + -8x * 4 + x2 * 4) = 3(x + -6)(x + 2)
(64 + -32x + 4x2) = 3(x + -6)(x + 2)

Reorder the terms:
64 + -32x + 4x2 = 3(-6 + x)(x + 2)

Reorder the terms:
64 + -32x + 4x2 = 3(-6 + x)(2 + x)

Multiply (-6 + x) * (2 + x)
64 + -32x + 4x2 = 3(-6(2 + x) + x(2 + x))
64 + -32x + 4x2 = 3((2 * -6 + x * -6) + x(2 + x))
64 + -32x + 4x2 = 3((-12 + -6x) + x(2 + x))
64 + -32x + 4x2 = 3(-12 + -6x + (2 * x + x * x))
64 + -32x + 4x2 = 3(-12 + -6x + (2x + x2))

Combine like terms: -6x + 2x = -4x
64 + -32x + 4x2 = 3(-12 + -4x + x2)
64 + -32x + 4x2 = (-12 * 3 + -4x * 3 + x2 * 3)
64 + -32x + 4x2 = (-36 + -12x + 3x2)

Solving
64 + -32x + 4x2 = -36 + -12x + 3x2

Solving for variable 'x'.

Reorder the terms:
64 + 36 + -32x + 12x + 4x2 + -3x2 = -36 + -12x + 3x2 + 36 + 12x + -3x2

Combine like terms: 64 + 36 = 100
100 + -32x + 12x + 4x2 + -3x2 = -36 + -12x + 3x2 + 36 + 12x + -3x2

Combine like terms: -32x + 12x = -20x
100 + -20x + 4x2 + -3x2 = -36 + -12x + 3x2 + 36 + 12x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
100 + -20x + 1x2 = -36 + -12x + 3x2 + 36 + 12x + -3x2

Reorder the terms:
100 + -20x + 1x2 = -36 + 36 + -12x + 12x + 3x2 + -3x2

Combine like terms: -36 + 36 = 0
100 + -20x + 1x2 = 0 + -12x + 12x + 3x2 + -3x2
100 + -20x + 1x2 = -12x + 12x + 3x2 + -3x2

Combine like terms: -12x + 12x = 0
100 + -20x + 1x2 = 0 + 3x2 + -3x2
100 + -20x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
100 + -20x + 1x2 = 0

Factor a trinomial.
(10 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {10, 10}

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