4(z^2+z-2)=-2z^2-7z+2

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


Simplifying
4(z2 + z + -2) = -2z2 + -7z + 2

Reorder the terms:
4(-2 + z + z2) = -2z2 + -7z + 2
(-2 * 4 + z * 4 + z2 * 4) = -2z2 + -7z + 2
(-8 + 4z + 4z2) = -2z2 + -7z + 2

Reorder the terms:
-8 + 4z + 4z2 = 2 + -7z + -2z2

Solving
-8 + 4z + 4z2 = 2 + -7z + -2z2

Solving for variable 'z'.

Reorder the terms:
-8 + -2 + 4z + 7z + 4z2 + 2z2 = 2 + -7z + -2z2 + -2 + 7z + 2z2

Combine like terms: -8 + -2 = -10
-10 + 4z + 7z + 4z2 + 2z2 = 2 + -7z + -2z2 + -2 + 7z + 2z2

Combine like terms: 4z + 7z = 11z
-10 + 11z + 4z2 + 2z2 = 2 + -7z + -2z2 + -2 + 7z + 2z2

Combine like terms: 4z2 + 2z2 = 6z2
-10 + 11z + 6z2 = 2 + -7z + -2z2 + -2 + 7z + 2z2

Reorder the terms:
-10 + 11z + 6z2 = 2 + -2 + -7z + 7z + -2z2 + 2z2

Combine like terms: 2 + -2 = 0
-10 + 11z + 6z2 = 0 + -7z + 7z + -2z2 + 2z2
-10 + 11z + 6z2 = -7z + 7z + -2z2 + 2z2

Combine like terms: -7z + 7z = 0
-10 + 11z + 6z2 = 0 + -2z2 + 2z2
-10 + 11z + 6z2 = -2z2 + 2z2

Combine like terms: -2z2 + 2z2 = 0
-10 + 11z + 6z2 = 0

Factor a trinomial.
(-5 + -2z)(2 + -3z) = 0


Subproblem 1
Set the factor '(-5 + -2z)' equal to zero and attempt to solve:

Simplifying
-5 + -2z = 0

Solving
-5 + -2z = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2z = 0 + 5
-2z = 0 + 5

Combine like terms: 0 + 5 = 5
-2z = 5

Divide each side by '-2'.
z = -2.5

Simplifying
z = -2.5

Subproblem 2
Set the factor '(2 + -3z)' equal to zero and attempt to solve:

Simplifying
2 + -3z = 0

Solving
2 + -3z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3z = 0 + -2
-3z = 0 + -2

Combine like terms: 0 + -2 = -2
-3z = -2

Divide each side by '-3'.
z = 0.6666666667

Simplifying
z = 0.6666666667
Solution
z = {-2.5, 0.6666666667}

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