4(3x-5)(2x+3)=25x^2-30x+9

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Solution for 4(3x-5)(2x+3)=25x^2-30x+9 equation: 


Simplifying
4(3x + -5)(2x + 3) = 25x2 + -30x + 9

Reorder the terms:
4(-5 + 3x)(2x + 3) = 25x2 + -30x + 9

Reorder the terms:
4(-5 + 3x)(3 + 2x) = 25x2 + -30x + 9

Multiply (-5 + 3x) * (3 + 2x)
4(-5(3 + 2x) + 3x * (3 + 2x)) = 25x2 + -30x + 9
4((3 * -5 + 2x * -5) + 3x * (3 + 2x)) = 25x2 + -30x + 9
4((-15 + -10x) + 3x * (3 + 2x)) = 25x2 + -30x + 9
4(-15 + -10x + (3 * 3x + 2x * 3x)) = 25x2 + -30x + 9
4(-15 + -10x + (9x + 6x2)) = 25x2 + -30x + 9

Combine like terms: -10x + 9x = -1x
4(-15 + -1x + 6x2) = 25x2 + -30x + 9
(-15 * 4 + -1x * 4 + 6x2 * 4) = 25x2 + -30x + 9
(-60 + -4x + 24x2) = 25x2 + -30x + 9

Reorder the terms:
-60 + -4x + 24x2 = 9 + -30x + 25x2

Solving
-60 + -4x + 24x2 = 9 + -30x + 25x2

Solving for variable 'x'.

Reorder the terms:
-60 + -9 + -4x + 30x + 24x2 + -25x2 = 9 + -30x + 25x2 + -9 + 30x + -25x2

Combine like terms: -60 + -9 = -69
-69 + -4x + 30x + 24x2 + -25x2 = 9 + -30x + 25x2 + -9 + 30x + -25x2

Combine like terms: -4x + 30x = 26x
-69 + 26x + 24x2 + -25x2 = 9 + -30x + 25x2 + -9 + 30x + -25x2

Combine like terms: 24x2 + -25x2 = -1x2
-69 + 26x + -1x2 = 9 + -30x + 25x2 + -9 + 30x + -25x2

Reorder the terms:
-69 + 26x + -1x2 = 9 + -9 + -30x + 30x + 25x2 + -25x2

Combine like terms: 9 + -9 = 0
-69 + 26x + -1x2 = 0 + -30x + 30x + 25x2 + -25x2
-69 + 26x + -1x2 = -30x + 30x + 25x2 + -25x2

Combine like terms: -30x + 30x = 0
-69 + 26x + -1x2 = 0 + 25x2 + -25x2
-69 + 26x + -1x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
-69 + 26x + -1x2 = 0

Factor a trinomial.
(-23 + x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-23 + x)' equal to zero and attempt to solve:

Simplifying
-23 + x = 0

Solving
-23 + x = 0

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

Add '23' to each side of the equation.
-23 + 23 + x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + x = 0 + 23
x = 0 + 23

Combine like terms: 0 + 23 = 23
x = 23

Simplifying
x = 23

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 = {23, 3}

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