4x(5x+1)=-x(7-x)

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Solution for 4x(5x+1)=-x(7-x) equation: 


Simplifying
4x(5x + 1) = -1x(7 + -1x)

Reorder the terms:
4x(1 + 5x) = -1x(7 + -1x)
(1 * 4x + 5x * 4x) = -1x(7 + -1x)
(4x + 20x2) = -1x(7 + -1x)
4x + 20x2 = (7 * -1x + -1x * -1x)
4x + 20x2 = (-7x + 1x2)

Solving
4x + 20x2 = -7x + 1x2

Solving for variable 'x'.

Reorder the terms:
4x + 7x + 20x2 + -1x2 = -7x + 1x2 + 7x + -1x2

Combine like terms: 4x + 7x = 11x
11x + 20x2 + -1x2 = -7x + 1x2 + 7x + -1x2

Combine like terms: 20x2 + -1x2 = 19x2
11x + 19x2 = -7x + 1x2 + 7x + -1x2

Reorder the terms:
11x + 19x2 = -7x + 7x + 1x2 + -1x2

Combine like terms: -7x + 7x = 0
11x + 19x2 = 0 + 1x2 + -1x2
11x + 19x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
11x + 19x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(11 + 19x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(11 + 19x)' equal to zero and attempt to solve:

Simplifying
11 + 19x = 0

Solving
11 + 19x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 19x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 19x = 0 + -11
19x = 0 + -11

Combine like terms: 0 + -11 = -11
19x = -11

Divide each side by '19'.
x = -0.5789473684

Simplifying
x = -0.5789473684
Solution
x = {0, -0.5789473684}

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