(2z+1)(2z-1)+12=4(z+5)-10

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Solution for (2z+1)(2z-1)+12=4(z+5)-10 equation: 


Simplifying
(2z + 1)(2z + -1) + 12 = 4(z + 5) + -10

Reorder the terms:
(1 + 2z)(2z + -1) + 12 = 4(z + 5) + -10

Reorder the terms:
(1 + 2z)(-1 + 2z) + 12 = 4(z + 5) + -10

Multiply (1 + 2z) * (-1 + 2z)
(1(-1 + 2z) + 2z * (-1 + 2z)) + 12 = 4(z + 5) + -10
((-1 * 1 + 2z * 1) + 2z * (-1 + 2z)) + 12 = 4(z + 5) + -10
((-1 + 2z) + 2z * (-1 + 2z)) + 12 = 4(z + 5) + -10
(-1 + 2z + (-1 * 2z + 2z * 2z)) + 12 = 4(z + 5) + -10
(-1 + 2z + (-2z + 4z2)) + 12 = 4(z + 5) + -10

Combine like terms: 2z + -2z = 0
(-1 + 0 + 4z2) + 12 = 4(z + 5) + -10
(-1 + 4z2) + 12 = 4(z + 5) + -10

Reorder the terms:
-1 + 12 + 4z2 = 4(z + 5) + -10

Combine like terms: -1 + 12 = 11
11 + 4z2 = 4(z + 5) + -10

Reorder the terms:
11 + 4z2 = 4(5 + z) + -10
11 + 4z2 = (5 * 4 + z * 4) + -10
11 + 4z2 = (20 + 4z) + -10

Reorder the terms:
11 + 4z2 = 20 + -10 + 4z

Combine like terms: 20 + -10 = 10
11 + 4z2 = 10 + 4z

Solving
11 + 4z2 = 10 + 4z

Solving for variable 'z'.

Reorder the terms:
11 + -10 + -4z + 4z2 = 10 + 4z + -10 + -4z

Combine like terms: 11 + -10 = 1
1 + -4z + 4z2 = 10 + 4z + -10 + -4z

Reorder the terms:
1 + -4z + 4z2 = 10 + -10 + 4z + -4z

Combine like terms: 10 + -10 = 0
1 + -4z + 4z2 = 0 + 4z + -4z
1 + -4z + 4z2 = 4z + -4z

Combine like terms: 4z + -4z = 0
1 + -4z + 4z2 = 0

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


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

Simplifying
1 + -2z = 0

Solving
1 + -2z = 0

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

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

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

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

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

Simplifying
z = 0.5

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

Simplifying
1 + -2z = 0

Solving
1 + -2z = 0

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

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

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

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

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

Simplifying
z = 0.5
Solution
z = {0.5, 0.5}

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