5(x+4)=7x(2x-4)

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Solution for 5(x+4)=7x(2x-4) equation:


Simplifying
5(x + 4) = 7x(2x + -4)

Reorder the terms:
5(4 + x) = 7x(2x + -4)
(4 * 5 + x * 5) = 7x(2x + -4)
(20 + 5x) = 7x(2x + -4)

Reorder the terms:
20 + 5x = 7x(-4 + 2x)
20 + 5x = (-4 * 7x + 2x * 7x)
20 + 5x = (-28x + 14x2)

Solving
20 + 5x = -28x + 14x2

Solving for variable 'x'.

Combine like terms: 5x + 28x = 33x
20 + 33x + -14x2 = -28x + 14x2 + 28x + -14x2

Reorder the terms:
20 + 33x + -14x2 = -28x + 28x + 14x2 + -14x2

Combine like terms: -28x + 28x = 0
20 + 33x + -14x2 = 0 + 14x2 + -14x2
20 + 33x + -14x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
20 + 33x + -14x2 = 0

Factor a trinomial.
(20 + -7x)(1 + 2x) = 0


Subproblem 1
Set the factor '(20 + -7x)' equal to zero and attempt to solve:

Simplifying
20 + -7x = 0

Solving
20 + -7x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -7x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -7x = 0 + -20
-7x = 0 + -20

Combine like terms: 0 + -20 = -20
-7x = -20

Divide each side by '-7'.
x = 2.857142857

Simplifying
x = 2.857142857

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {2.857142857, -0.5}

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