4(x+2)(-3x+5)=3x^2+4x-36

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Solution for 4(x+2)(-3x+5)=3x^2+4x-36 equation: 


Simplifying
4(x + 2)(-3x + 5) = 3x2 + 4x + -36

Reorder the terms:
4(2 + x)(-3x + 5) = 3x2 + 4x + -36

Reorder the terms:
4(2 + x)(5 + -3x) = 3x2 + 4x + -36

Multiply (2 + x) * (5 + -3x)
4(2(5 + -3x) + x(5 + -3x)) = 3x2 + 4x + -36
4((5 * 2 + -3x * 2) + x(5 + -3x)) = 3x2 + 4x + -36
4((10 + -6x) + x(5 + -3x)) = 3x2 + 4x + -36
4(10 + -6x + (5 * x + -3x * x)) = 3x2 + 4x + -36
4(10 + -6x + (5x + -3x2)) = 3x2 + 4x + -36

Combine like terms: -6x + 5x = -1x
4(10 + -1x + -3x2) = 3x2 + 4x + -36
(10 * 4 + -1x * 4 + -3x2 * 4) = 3x2 + 4x + -36
(40 + -4x + -12x2) = 3x2 + 4x + -36

Reorder the terms:
40 + -4x + -12x2 = -36 + 4x + 3x2

Solving
40 + -4x + -12x2 = -36 + 4x + 3x2

Solving for variable 'x'.

Reorder the terms:
40 + 36 + -4x + -4x + -12x2 + -3x2 = -36 + 4x + 3x2 + 36 + -4x + -3x2

Combine like terms: 40 + 36 = 76
76 + -4x + -4x + -12x2 + -3x2 = -36 + 4x + 3x2 + 36 + -4x + -3x2

Combine like terms: -4x + -4x = -8x
76 + -8x + -12x2 + -3x2 = -36 + 4x + 3x2 + 36 + -4x + -3x2

Combine like terms: -12x2 + -3x2 = -15x2
76 + -8x + -15x2 = -36 + 4x + 3x2 + 36 + -4x + -3x2

Reorder the terms:
76 + -8x + -15x2 = -36 + 36 + 4x + -4x + 3x2 + -3x2

Combine like terms: -36 + 36 = 0
76 + -8x + -15x2 = 0 + 4x + -4x + 3x2 + -3x2
76 + -8x + -15x2 = 4x + -4x + 3x2 + -3x2

Combine like terms: 4x + -4x = 0
76 + -8x + -15x2 = 0 + 3x2 + -3x2
76 + -8x + -15x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
76 + -8x + -15x2 = 0

Factor a trinomial.
(2 + -1x)(38 + 15x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(38 + 15x)' equal to zero and attempt to solve:

Simplifying
38 + 15x = 0

Solving
38 + 15x = 0

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

Add '-38' to each side of the equation.
38 + -38 + 15x = 0 + -38

Combine like terms: 38 + -38 = 0
0 + 15x = 0 + -38
15x = 0 + -38

Combine like terms: 0 + -38 = -38
15x = -38

Divide each side by '15'.
x = -2.533333333

Simplifying
x = -2.533333333
Solution
x = {2, -2.533333333}

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