0=4(2x-3)(x+7)

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Solution for 0=4(2x-3)(x+7) equation: 


Simplifying
0 = 4(2x + -3)(x + 7)

Reorder the terms:
0 = 4(-3 + 2x)(x + 7)

Reorder the terms:
0 = 4(-3 + 2x)(7 + x)

Multiply (-3 + 2x) * (7 + x)
0 = 4(-3(7 + x) + 2x * (7 + x))
0 = 4((7 * -3 + x * -3) + 2x * (7 + x))
0 = 4((-21 + -3x) + 2x * (7 + x))
0 = 4(-21 + -3x + (7 * 2x + x * 2x))
0 = 4(-21 + -3x + (14x + 2x2))

Combine like terms: -3x + 14x = 11x
0 = 4(-21 + 11x + 2x2)
0 = (-21 * 4 + 11x * 4 + 2x2 * 4)
0 = (-84 + 44x + 8x2)

Solving
0 = -84 + 44x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + 84 = 84
84 + -44x + -8x2 = -84 + 44x + 8x2 + 84 + -44x + -8x2

Reorder the terms:
84 + -44x + -8x2 = -84 + 84 + 44x + -44x + 8x2 + -8x2

Combine like terms: -84 + 84 = 0
84 + -44x + -8x2 = 0 + 44x + -44x + 8x2 + -8x2
84 + -44x + -8x2 = 44x + -44x + 8x2 + -8x2

Combine like terms: 44x + -44x = 0
84 + -44x + -8x2 = 0 + 8x2 + -8x2
84 + -44x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
84 + -44x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(21 + -11x + -2x2) = 0

Factor a trinomial.
4((3 + -2x)(7 + x)) = 0

Ignore the factor 4.

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

Simplifying
x = -7
Solution
x = {1.5, -7}

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