4(x+5)(2x-3)=96

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Solution for 4(x+5)(2x-3)=96 equation: 


Simplifying
4(x + 5)(2x + -3) = 96

Reorder the terms:
4(5 + x)(2x + -3) = 96

Reorder the terms:
4(5 + x)(-3 + 2x) = 96

Multiply (5 + x) * (-3 + 2x)
4(5(-3 + 2x) + x(-3 + 2x)) = 96
4((-3 * 5 + 2x * 5) + x(-3 + 2x)) = 96
4((-15 + 10x) + x(-3 + 2x)) = 96
4(-15 + 10x + (-3 * x + 2x * x)) = 96
4(-15 + 10x + (-3x + 2x2)) = 96

Combine like terms: 10x + -3x = 7x
4(-15 + 7x + 2x2) = 96
(-15 * 4 + 7x * 4 + 2x2 * 4) = 96
(-60 + 28x + 8x2) = 96

Solving
-60 + 28x + 8x2 = 96

Solving for variable 'x'.

Reorder the terms:
-60 + -96 + 28x + 8x2 = 96 + -96

Combine like terms: -60 + -96 = -156
-156 + 28x + 8x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-156 + 28x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-39 + 7x + 2x2) = 0

Factor a trinomial.
4((-13 + -2x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve:

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5

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 = {-6.5, 3}

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