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

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


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

Reorder the terms:
2x(-4 + x) = 5x + 7
(-4 * 2x + x * 2x) = 5x + 7
(-8x + 2x2) = 5x + 7

Reorder the terms:
-8x + 2x2 = 7 + 5x

Solving
-8x + 2x2 = 7 + 5x

Solving for variable 'x'.

Reorder the terms:
-7 + -8x + -5x + 2x2 = 7 + 5x + -7 + -5x

Combine like terms: -8x + -5x = -13x
-7 + -13x + 2x2 = 7 + 5x + -7 + -5x

Reorder the terms:
-7 + -13x + 2x2 = 7 + -7 + 5x + -5x

Combine like terms: 7 + -7 = 0
-7 + -13x + 2x2 = 0 + 5x + -5x
-7 + -13x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-7 + -13x + 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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