5(x-4)(x+7)=0

Solution for 5(x-4)(x+7)=0 equation:

Simplifying
5(x + -4)(x + 7) = 0

Reorder the terms:
5(-4 + x)(x + 7) = 0

Reorder the terms:
5(-4 + x)(7 + x) = 0

Multiply (-4 + x) * (7 + x)
5(-4(7 + x) + x(7 + x)) = 0
5((7 * -4 + x * -4) + x(7 + x)) = 0
5((-28 + -4x) + x(7 + x)) = 0
5(-28 + -4x + (7 * x + x * x)) = 0
5(-28 + -4x + (7x + x2)) = 0

Combine like terms: -4x + 7x = 3x
5(-28 + 3x + x2) = 0
(-28 * 5 + 3x * 5 + x2 * 5) = 0
(-140 + 15x + 5x2) = 0

Solving
-140 + 15x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-28 + 3x + x2) = 0

Factor a trinomial.
5((-7 + -1x)(4 + -1x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-7, 4}