=2z^2+7z-4

Solution for =2z^2+7z-4 equation:

Simplifying
0 = 2z2 + 7z + -4

Reorder the terms:
0 = -4 + 7z + 2z2

Solving
0 = -4 + 7z + 2z2

Solving for variable 'z'.

Combine like terms: 0 + 4 = 4
4 + -7z + -2z2 = -4 + 7z + 2z2 + 4 + -7z + -2z2

Reorder the terms:
4 + -7z + -2z2 = -4 + 4 + 7z + -7z + 2z2 + -2z2

Combine like terms: -4 + 4 = 0
4 + -7z + -2z2 = 0 + 7z + -7z + 2z2 + -2z2
4 + -7z + -2z2 = 7z + -7z + 2z2 + -2z2

Combine like terms: 7z + -7z = 0
4 + -7z + -2z2 = 0 + 2z2 + -2z2
4 + -7z + -2z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
4 + -7z + -2z2 = 0

Factor a trinomial.
(1 + -2z)(4 + z) = 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 '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

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

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

Simplifying
z = -4
Solution
z = {0.5, -4}