8(x-4)+3(8x)=7x(x-4)

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Solution for 8(x-4)+3(8x)=7x(x-4) equation: 


Simplifying
8(x + -4) + 3(8x) = 7x(x + -4)

Reorder the terms:
8(-4 + x) + 3(8x) = 7x(x + -4)
(-4 * 8 + x * 8) + 3(8x) = 7x(x + -4)
(-32 + 8x) + 3(8x) = 7x(x + -4)

Remove parenthesis around (8x)
-32 + 8x + 3 * 8x = 7x(x + -4)

Multiply 3 * 8
-32 + 8x + 24x = 7x(x + -4)

Combine like terms: 8x + 24x = 32x
-32 + 32x = 7x(x + -4)

Reorder the terms:
-32 + 32x = 7x(-4 + x)
-32 + 32x = (-4 * 7x + x * 7x)
-32 + 32x = (-28x + 7x2)

Solving
-32 + 32x = -28x + 7x2

Solving for variable 'x'.

Combine like terms: 32x + 28x = 60x
-32 + 60x + -7x2 = -28x + 7x2 + 28x + -7x2

Reorder the terms:
-32 + 60x + -7x2 = -28x + 28x + 7x2 + -7x2

Combine like terms: -28x + 28x = 0
-32 + 60x + -7x2 = 0 + 7x2 + -7x2
-32 + 60x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-32 + 60x + -7x2 = 0

Factor a trinomial.
(-8 + x)(4 + -7x) = 0


Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(4 + -7x)' equal to zero and attempt to solve:

Simplifying
4 + -7x = 0

Solving
4 + -7x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7x = 0 + -4
-7x = 0 + -4

Combine like terms: 0 + -4 = -4
-7x = -4

Divide each side by '-7'.
x = 0.5714285714

Simplifying
x = 0.5714285714
Solution
x = {8, 0.5714285714}

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