3(x-5)(x-7)=4(x+3)

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Solution for 3(x-5)(x-7)=4(x+3) equation: 


Simplifying
3(x + -5)(x + -7) = 4(x + 3)

Reorder the terms:
3(-5 + x)(x + -7) = 4(x + 3)

Reorder the terms:
3(-5 + x)(-7 + x) = 4(x + 3)

Multiply (-5 + x) * (-7 + x)
3(-5(-7 + x) + x(-7 + x)) = 4(x + 3)
3((-7 * -5 + x * -5) + x(-7 + x)) = 4(x + 3)
3((35 + -5x) + x(-7 + x)) = 4(x + 3)
3(35 + -5x + (-7 * x + x * x)) = 4(x + 3)
3(35 + -5x + (-7x + x2)) = 4(x + 3)

Combine like terms: -5x + -7x = -12x
3(35 + -12x + x2) = 4(x + 3)
(35 * 3 + -12x * 3 + x2 * 3) = 4(x + 3)
(105 + -36x + 3x2) = 4(x + 3)

Reorder the terms:
105 + -36x + 3x2 = 4(3 + x)
105 + -36x + 3x2 = (3 * 4 + x * 4)
105 + -36x + 3x2 = (12 + 4x)

Solving
105 + -36x + 3x2 = 12 + 4x

Solving for variable 'x'.

Reorder the terms:
105 + -12 + -36x + -4x + 3x2 = 12 + 4x + -12 + -4x

Combine like terms: 105 + -12 = 93
93 + -36x + -4x + 3x2 = 12 + 4x + -12 + -4x

Combine like terms: -36x + -4x = -40x
93 + -40x + 3x2 = 12 + 4x + -12 + -4x

Reorder the terms:
93 + -40x + 3x2 = 12 + -12 + 4x + -4x

Combine like terms: 12 + -12 = 0
93 + -40x + 3x2 = 0 + 4x + -4x
93 + -40x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
93 + -40x + 3x2 = 0

Factor a trinomial.
(3 + -1x)(31 + -3x) = 0


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 '(31 + -3x)' equal to zero and attempt to solve:

Simplifying
31 + -3x = 0

Solving
31 + -3x = 0

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

Add '-31' to each side of the equation.
31 + -31 + -3x = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -3x = 0 + -31
-3x = 0 + -31

Combine like terms: 0 + -31 = -31
-3x = -31

Divide each side by '-3'.
x = 10.33333333

Simplifying
x = 10.33333333
Solution
x = {3, 10.33333333}

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