4-(2x+3)(5x-2)=13

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Solution for 4-(2x+3)(5x-2)=13 equation: 


Simplifying
4 + -1(2x + 3)(5x + -2) = 13

Reorder the terms:
4 + -1(3 + 2x)(5x + -2) = 13

Reorder the terms:
4 + -1(3 + 2x)(-2 + 5x) = 13

Multiply (3 + 2x) * (-2 + 5x)
4 + -1(3(-2 + 5x) + 2x * (-2 + 5x)) = 13
4 + -1((-2 * 3 + 5x * 3) + 2x * (-2 + 5x)) = 13
4 + -1((-6 + 15x) + 2x * (-2 + 5x)) = 13
4 + -1(-6 + 15x + (-2 * 2x + 5x * 2x)) = 13
4 + -1(-6 + 15x + (-4x + 10x2)) = 13

Combine like terms: 15x + -4x = 11x
4 + -1(-6 + 11x + 10x2) = 13
4 + (-6 * -1 + 11x * -1 + 10x2 * -1) = 13
4 + (6 + -11x + -10x2) = 13

Combine like terms: 4 + 6 = 10
10 + -11x + -10x2 = 13

Solving
10 + -11x + -10x2 = 13

Solving for variable 'x'.

Reorder the terms:
10 + -13 + -11x + -10x2 = 13 + -13

Combine like terms: 10 + -13 = -3
-3 + -11x + -10x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-3 + -11x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 11x + 10x2) = 0

Factor a trinomial.
-1((3 + 5x)(1 + 2x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + 5x)' equal to zero and attempt to solve:

Simplifying
3 + 5x = 0

Solving
3 + 5x = 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 + 5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5x = 0 + -3
5x = 0 + -3

Combine like terms: 0 + -3 = -3
5x = -3

Divide each side by '5'.
x = -0.6

Simplifying
x = -0.6

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

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

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-0.6, -0.5}

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