4x(x-7)=(2x+1)(x-7)

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Solution for 4x(x-7)=(2x+1)(x-7) equation: 


Simplifying
4x(x + -7) = (2x + 1)(x + -7)

Reorder the terms:
4x(-7 + x) = (2x + 1)(x + -7)
(-7 * 4x + x * 4x) = (2x + 1)(x + -7)
(-28x + 4x2) = (2x + 1)(x + -7)

Reorder the terms:
-28x + 4x2 = (1 + 2x)(x + -7)

Reorder the terms:
-28x + 4x2 = (1 + 2x)(-7 + x)

Multiply (1 + 2x) * (-7 + x)
-28x + 4x2 = (1(-7 + x) + 2x * (-7 + x))
-28x + 4x2 = ((-7 * 1 + x * 1) + 2x * (-7 + x))
-28x + 4x2 = ((-7 + 1x) + 2x * (-7 + x))
-28x + 4x2 = (-7 + 1x + (-7 * 2x + x * 2x))
-28x + 4x2 = (-7 + 1x + (-14x + 2x2))

Combine like terms: 1x + -14x = -13x
-28x + 4x2 = (-7 + -13x + 2x2)

Solving
-28x + 4x2 = -7 + -13x + 2x2

Solving for variable 'x'.

Reorder the terms:
7 + -28x + 13x + 4x2 + -2x2 = -7 + -13x + 2x2 + 7 + 13x + -2x2

Combine like terms: -28x + 13x = -15x
7 + -15x + 4x2 + -2x2 = -7 + -13x + 2x2 + 7 + 13x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
7 + -15x + 2x2 = -7 + -13x + 2x2 + 7 + 13x + -2x2

Reorder the terms:
7 + -15x + 2x2 = -7 + 7 + -13x + 13x + 2x2 + -2x2

Combine like terms: -7 + 7 = 0
7 + -15x + 2x2 = 0 + -13x + 13x + 2x2 + -2x2
7 + -15x + 2x2 = -13x + 13x + 2x2 + -2x2

Combine like terms: -13x + 13x = 0
7 + -15x + 2x2 = 0 + 2x2 + -2x2
7 + -15x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
7 + -15x + 2x2 = 0

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


Subproblem 1
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

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 = {0.5, 7}

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