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

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


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

Reorder the terms:
4x(-7 + x) = (3x + -3)(x + -7)
(-7 * 4x + x * 4x) = (3x + -3)(x + -7)
(-28x + 4x2) = (3x + -3)(x + -7)

Reorder the terms:
-28x + 4x2 = (-3 + 3x)(x + -7)

Reorder the terms:
-28x + 4x2 = (-3 + 3x)(-7 + x)

Multiply (-3 + 3x) * (-7 + x)
-28x + 4x2 = (-3(-7 + x) + 3x * (-7 + x))
-28x + 4x2 = ((-7 * -3 + x * -3) + 3x * (-7 + x))
-28x + 4x2 = ((21 + -3x) + 3x * (-7 + x))
-28x + 4x2 = (21 + -3x + (-7 * 3x + x * 3x))
-28x + 4x2 = (21 + -3x + (-21x + 3x2))

Combine like terms: -3x + -21x = -24x
-28x + 4x2 = (21 + -24x + 3x2)

Solving
-28x + 4x2 = 21 + -24x + 3x2

Solving for variable 'x'.

Reorder the terms:
-21 + -28x + 24x + 4x2 + -3x2 = 21 + -24x + 3x2 + -21 + 24x + -3x2

Combine like terms: -28x + 24x = -4x
-21 + -4x + 4x2 + -3x2 = 21 + -24x + 3x2 + -21 + 24x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-21 + -4x + 1x2 = 21 + -24x + 3x2 + -21 + 24x + -3x2

Reorder the terms:
-21 + -4x + 1x2 = 21 + -21 + -24x + 24x + 3x2 + -3x2

Combine like terms: 21 + -21 = 0
-21 + -4x + 1x2 = 0 + -24x + 24x + 3x2 + -3x2
-21 + -4x + 1x2 = -24x + 24x + 3x2 + -3x2

Combine like terms: -24x + 24x = 0
-21 + -4x + 1x2 = 0 + 3x2 + -3x2
-21 + -4x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-21 + -4x + 1x2 = 0

Factor a trinomial.
(-3 + -1x)(7 + -1x) = 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-3, 7}

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