1.5(168)=(2x+4)(x+7)

Solution for 1.5(168)=(2x+4)(x+7) equation:

Simplifying
1.5(168) = (2x + 4)(x + 7)

Multiply 1.5 * 168
252 = (2x + 4)(x + 7)

Reorder the terms:
252 = (4 + 2x)(x + 7)

Reorder the terms:
252 = (4 + 2x)(7 + x)

Multiply (4 + 2x) * (7 + x)
252 = (4(7 + x) + 2x * (7 + x))
252 = ((7 * 4 + x * 4) + 2x * (7 + x))
252 = ((28 + 4x) + 2x * (7 + x))
252 = (28 + 4x + (7 * 2x + x * 2x))
252 = (28 + 4x + (14x + 2x2))

Combine like terms: 4x + 14x = 18x
252 = (28 + 18x + 2x2)

Solving
252 = 28 + 18x + 2x2

Solving for variable 'x'.

Combine like terms: 252 + -28 = 224
224 + -18x + -2x2 = 28 + 18x + 2x2 + -28 + -18x + -2x2

Reorder the terms:
224 + -18x + -2x2 = 28 + -28 + 18x + -18x + 2x2 + -2x2

Combine like terms: 28 + -28 = 0
224 + -18x + -2x2 = 0 + 18x + -18x + 2x2 + -2x2
224 + -18x + -2x2 = 18x + -18x + 2x2 + -2x2

Combine like terms: 18x + -18x = 0
224 + -18x + -2x2 = 0 + 2x2 + -2x2
224 + -18x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
224 + -18x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(112 + -9x + -1x2) = 0

Factor a trinomial.
2((7 + -1x)(16 + x)) = 0

Ignore the factor 2.
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 '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {7, -16}