(z-4)(z+3)=-10

Solution for (z-4)(z+3)=-10 equation:

Simplifying
(z + -4)(z + 3) = -10

Reorder the terms:
(-4 + z)(z + 3) = -10

Reorder the terms:
(-4 + z)(3 + z) = -10

Multiply (-4 + z) * (3 + z)
(-4(3 + z) + z(3 + z)) = -10
((3 * -4 + z * -4) + z(3 + z)) = -10
((-12 + -4z) + z(3 + z)) = -10
(-12 + -4z + (3 * z + z * z)) = -10
(-12 + -4z + (3z + z2)) = -10

Combine like terms: -4z + 3z = -1z
(-12 + -1z + z2) = -10

Solving
-12 + -1z + z2 = -10

Solving for variable 'z'.

Reorder the terms:
-12 + 10 + -1z + z2 = -10 + 10

Combine like terms: -12 + 10 = -2
-2 + -1z + z2 = -10 + 10

Combine like terms: -10 + 10 = 0
-2 + -1z + z2 = 0

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

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

Simplifying
-1 + -1z = 0

Solving
-1 + -1z = 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 + -1z = 0 + 1

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

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

Divide each side by '-1'.
z = -1

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-1, 2}