(-5z+1)(16z+2)=2+(-2z+4)(40z+4)+7z

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Solution for (-5z+1)(16z+2)=2+(-2z+4)(40z+4)+7z equation:


Simplifying
(-5z + 1)(16z + 2) = 2 + (-2z + 4)(40z + 4) + 7z

Reorder the terms:
(1 + -5z)(16z + 2) = 2 + (-2z + 4)(40z + 4) + 7z

Reorder the terms:
(1 + -5z)(2 + 16z) = 2 + (-2z + 4)(40z + 4) + 7z

Multiply (1 + -5z) * (2 + 16z)
(1(2 + 16z) + -5z * (2 + 16z)) = 2 + (-2z + 4)(40z + 4) + 7z
((2 * 1 + 16z * 1) + -5z * (2 + 16z)) = 2 + (-2z + 4)(40z + 4) + 7z
((2 + 16z) + -5z * (2 + 16z)) = 2 + (-2z + 4)(40z + 4) + 7z
(2 + 16z + (2 * -5z + 16z * -5z)) = 2 + (-2z + 4)(40z + 4) + 7z
(2 + 16z + (-10z + -80z2)) = 2 + (-2z + 4)(40z + 4) + 7z

Combine like terms: 16z + -10z = 6z
(2 + 6z + -80z2) = 2 + (-2z + 4)(40z + 4) + 7z

Reorder the terms:
2 + 6z + -80z2 = 2 + (4 + -2z)(40z + 4) + 7z

Reorder the terms:
2 + 6z + -80z2 = 2 + (4 + -2z)(4 + 40z) + 7z

Multiply (4 + -2z) * (4 + 40z)
2 + 6z + -80z2 = 2 + (4(4 + 40z) + -2z * (4 + 40z)) + 7z
2 + 6z + -80z2 = 2 + ((4 * 4 + 40z * 4) + -2z * (4 + 40z)) + 7z
2 + 6z + -80z2 = 2 + ((16 + 160z) + -2z * (4 + 40z)) + 7z
2 + 6z + -80z2 = 2 + (16 + 160z + (4 * -2z + 40z * -2z)) + 7z
2 + 6z + -80z2 = 2 + (16 + 160z + (-8z + -80z2)) + 7z

Combine like terms: 160z + -8z = 152z
2 + 6z + -80z2 = 2 + (16 + 152z + -80z2) + 7z

Reorder the terms:
2 + 6z + -80z2 = 2 + 16 + 152z + 7z + -80z2

Combine like terms: 2 + 16 = 18
2 + 6z + -80z2 = 18 + 152z + 7z + -80z2

Combine like terms: 152z + 7z = 159z
2 + 6z + -80z2 = 18 + 159z + -80z2

Add '80z2' to each side of the equation.
2 + 6z + -80z2 + 80z2 = 18 + 159z + -80z2 + 80z2

Combine like terms: -80z2 + 80z2 = 0
2 + 6z + 0 = 18 + 159z + -80z2 + 80z2
2 + 6z = 18 + 159z + -80z2 + 80z2

Combine like terms: -80z2 + 80z2 = 0
2 + 6z = 18 + 159z + 0
2 + 6z = 18 + 159z

Solving
2 + 6z = 18 + 159z

Solving for variable 'z'.

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

Add '-159z' to each side of the equation.
2 + 6z + -159z = 18 + 159z + -159z

Combine like terms: 6z + -159z = -153z
2 + -153z = 18 + 159z + -159z

Combine like terms: 159z + -159z = 0
2 + -153z = 18 + 0
2 + -153z = 18

Add '-2' to each side of the equation.
2 + -2 + -153z = 18 + -2

Combine like terms: 2 + -2 = 0
0 + -153z = 18 + -2
-153z = 18 + -2

Combine like terms: 18 + -2 = 16
-153z = 16

Divide each side by '-153'.
z = -0.1045751634

Simplifying
z = -0.1045751634

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