=7(x-4)(x-3)

Solution for =7(x-4)(x-3) equation:

Simplifying
0 = 7(x + -4)(x + -3)

Reorder the terms:
0 = 7(-4 + x)(x + -3)

Reorder the terms:
0 = 7(-4 + x)(-3 + x)

Multiply (-4 + x) * (-3 + x)
0 = 7(-4(-3 + x) + x(-3 + x))
0 = 7((-3 * -4 + x * -4) + x(-3 + x))
0 = 7((12 + -4x) + x(-3 + x))
0 = 7(12 + -4x + (-3 * x + x * x))
0 = 7(12 + -4x + (-3x + x2))

Combine like terms: -4x + -3x = -7x
0 = 7(12 + -7x + x2)
0 = (12 * 7 + -7x * 7 + x2 * 7)
0 = (84 + -49x + 7x2)

Solving
0 = 84 + -49x + 7x2

Solving for variable 'x'.

Combine like terms: 0 + -84 = -84
-84 + 49x + -7x2 = 84 + -49x + 7x2 + -84 + 49x + -7x2

Reorder the terms:
-84 + 49x + -7x2 = 84 + -84 + -49x + 49x + 7x2 + -7x2

Combine like terms: 84 + -84 = 0
-84 + 49x + -7x2 = 0 + -49x + 49x + 7x2 + -7x2
-84 + 49x + -7x2 = -49x + 49x + 7x2 + -7x2

Combine like terms: -49x + 49x = 0
-84 + 49x + -7x2 = 0 + 7x2 + -7x2
-84 + 49x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-84 + 49x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-12 + 7x + -1x2) = 0

Factor a trinomial.
7((-4 + x)(3 + -1x)) = 0

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

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

Simplifying
x = 4
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {4, 3}